arXiv subjects

Steven R. Spangler

Publications and source records attributed to Steven R. Spangler.

At least 19 recordsLinked to original sources

arXiv2026

Upper Limits to Long-Term Variability of Solar-Type Stars from Observations of the Open Cluster M67

Variations in the luminosity of the Sun on timescales of thousands to millions of years could potentially be responsible for terrestrial climate variations in the Phanerozooic geological period (last 540 million years). In this paper, I consider a method that utilizes observations of an open star cluster with approximately the age of the Sun, specifically M67, with data taken from Geller (2015). The idea is to measure the width of the main sequence in the region of solar-type stars, here generously defined to be about spectral class G0 - K1. This width gives an estimate of the dispersion in absolute magnitude of nominally solar-type stars. The sample used consists of 170 solar-type main sequence stars which are not known to be binaries. With this sample, I form an empirical measurement of the width of the main sequence, which is compared with a theoretical expression from Spangler (2025). The measured spread is consistent with a value of sigma, the normalized Gaussian variability of the primary and (if present) secondary star, in the range of 0.100 - 0.135. However, the expected value of sigma from purely photometric noise is estimated as 0.101. Generous upper limits to the intrinsic variability contribution to the inferred width are sigma in the range 0.058-0.089. These limits are not totally devoid of interest in a paleoclimatic context. However, major improvements in the technique are possible with the use of existing data sets from space astronomy missions such as Gaia and Kepler.

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arXiv2025

The Effect of Photometric Errors on the Measured Width of the Main Sequence in Star Clusters

This paper deals with the effect of errors in the B and V magnitudes, or measurements in any other color system, on the width of the main sequence in a color-magnitude (Hertzsprung-Russell) diagram. The width is defined as the dispersion in apparent (or absolute) magnitude at a fixed, measured photometric color. I find that the dispersion is larger than might be thought, a priori. A statistical analysis is presented which demonstrates that the error in the magnitude residual from a linear approximation to the main sequence is Gaussian, but with a standard deviation which is much larger, in general, than the errors in the individual B and V magnitudes. This result is confirmed by a Monte Carlo simulation of a main sequence population with specified errors in B and V magnitudes, and can be explained on the basis of simple algebraic arguments.

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arXiv2025

Broadening of the Main Sequence of a Star Cluster by Undetected Binaries

This paper is concerned with the spread in apparent magnitudes (or absolute magnitudes) of main-sequence stars in a star cluster. I specifically consider the effect of binary stars in broadening the main sequence. I present analytic and semi-analytic expressions for the probability density function (pdf) of the magnitude at a given photometric color, including the effects of binarity. The expressions obtained employ plausible models for the pdfs of the magnitudes of the primary and secondary stars, as well as the distribution of secondary-to-primary mass ratio. A crucial parameter is the fraction of stars in the star cluster that are binaries. The resultant formulas can be used to determine the fraction of binaries in a sample of stars taken from a star cluster, or to limit long term variations in the luminosity of solar type stars.

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arXiv2022

On the Measurement of Vorticity in Astrophysical Fluids

Vorticity is central to the nature of, and dynamical processes in turbulence, including turbulence in astrophysical fluids. The results of \cite{Raymond20a,Raymond20b} on vorticity in the post-shock fluid of the Cygnus Loop supernova remnant are therefore of great interest. We consider the degree to which spectroscopic measurements of an optically-thin line, the most common type of astronomical velocimetry, can yield unambiguous measurements of the vorticity in a fluid. We consider an ideal case of observations in the plane of a flow which may or may not contain vorticity. In one case, the flow possesses vorticity in a direction perpendicular to the plane of observations. In the other case, the flow is irrotational (zero vorticity) by construction. The observationally-deduced vorticity (referred to as the {\em pseudovorticity}) is inferred from spatial differences in the line-of-sight component of velocity, and assumptions of symmetry. My principal result is that in the case of the vortical flow, the pseudovorticity is a reasonable match for the true vorticity. However, and importantly, the pseudovorticity in the case of the irrotational flow field is also nonzero, and comparable in magnitude to that for a vortical flow. The conclusion of this paper is that while astronomical spectroscopic observations may yield a good estimate of the vorticity in a remote fluid, the robustness of such an inference cannot be insured.

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arXiv2021

A Method for a Pseudo-Local Measurement of the Galactic Magnetic Field

Much of the information about the magnetic field in the Milky Way and other galaxies comes from measurements which are path integrals, such as Faraday rotation and the polarization of synchrotron radiation of cosmic ray electrons. The measurement made at the radio telescope results from the contributions of volume elements along a long line of sight. The inferred magnetic field is therefore some sort of average over a long line segment. A magnetic field measurement at a given spatial location is of much more physical significance. In this paper, we point out that HII regions fortuitously offer such a ``point'' measurement, albeit of one component of the magnetic field, and averaged over the sightline through the HII region. However, the line of sight (LOS) through an HII region is much smaller (e.g. 30 - 50 pc) than one through the entire Galactic disk, and thus constitutes a ``pseudo-local'' measurement. We use published HII region Faraday rotation measurements to provide a new constraint on the magnitude of magnetohydrodynamic (MHD) turbulence in the Galaxy, as well as to raise intriguing speculations about the modification of the Galactic field during the star formation process.

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arXiv2019

Realistic Models for Filling and Abundance Discrepancy Factors in Photoionised Nebulae

When comparing nebular electron densities derived from collisionally excited lines (CELs) to those estimated using the emission measure, significant discrepancies are common. The standard solution is to view nebulae as aggregates of dense regions of constant density in an otherwise empty void. This porosity is parametrized by a filling factor $f<1$. Similarly, abundance and temperature discrepancies between optical recombination lines (ORLs) and CELs are often explained by invoking a dual delta distribution of a dense, cool, metal-rich component immersed in a diffuse, warm, metal-poor plasma. In this paper, we examine the possibility that the observational diagnostics that lead to such discrepancies can be produced by a realistic distribution of density and temperature fluctuations, such as might arise in plasma turbulence. We produce simulated nebulae with density and temperature fluctuations described by various probability distribution functions (pdfs). Standard astronomical diagnostics are applied to these simulated observations to derive estimates of nebular densities, temperatures, and abundances. Our results show that for plausible density pdfs the simulated observations lead to filling factors in the observed range. None of our simulations satisfactorily reproduce the abundance discrepancy factors (ADFs) in planetary nebulae, although there is possible consistency with \ion{H}{ii} regions. Compared to the case of density-only and temperature-only fluctuations, a positive correlation between density and temperature reduces the filling factor and ADF (from optical CELs), whereas a negative correlation increases both, eventually causing the filling factor to exceed unity. This result suggests that real observations can provide constraints on the thermodynamics of small scale fluctuations.

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arXiv2019

Analytic Estimates of the Effect of Plasma Density Fluctuations on HII Region Density Diagnostics

An analytic calculation is made of the effect of plasma density fluctuations on some spectroscopic diagnostics commonly used in the study of HII regions and planetary nebulae. To permit an analytic treatment, attention is restricted to the case of density fluctuations possessing an exponential probability distribution function (pdf). The present investigation is made in support of a completely numerical and more extensive study of nebular diagnostics by Bergerud et al (2019). Results from this paper are presented in terms of graphs of the observed quantity (spectroscopic line ratio) versus mean nebular density. Our results yield a higher density estimate, given the same observed line ratio, for the case of a nebula with density fluctuations than for the case of a nebula with uniform density. This is qualitatively consistent with the typically observed case, in which the observations lead to the inference of a filling factor < 1. Our results are in quantitative agreement with those of Bergerud et al (2019), and thus corroborate those calculations for the case of an exponential pdf.

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arXiv2018

A Faraday Rotation Study of the Stellar Bubble and HII Region Associated with the W4 Complex

We utilized the Very Large Array to make multifrequency polarization measurements of 20 radio sources viewed through the IC 1805 HII region and "Superbubble", as well as in the immediate vicinity. The measurements at frequencies between 4.33 and 7.76 GHz yield Faraday rotation measures along 27 lines of sight to these sources (some sources have more than one component). The Faraday rotation measures (RM) are used to probe the plasma structure of the IC 1805 HII region and to test the degree to which the Galactic magnetic field is heavily modified (amplified) by the dynamics of the HII region. We find that similar to the Rosette Nebula (Savage et al. 2013, Costa et al. 2016) and the Cygnus OB1 association (Whiting et al. 2009), IC 1805 constitutes a "Faraday rotation anomaly", or a region of increased RM relative to the general Galactic background value. Although the RM observed on lines of sight through the region vary substantially, the |RM| due to the nebula is commonly 600 -- 800 rad m^-2. In spite of this, the observed RMs are not as large as simple, analytic models of magnetic field amplification in HII regions might indicate. This suggests that the Galactic field is not increased by a substantial factor within the ionized gas in an HII region. We also find that with one exception, the sign of the RM for all sources is that expected for the polarity of the Galactic field in this direction. The same behavior was found for the Rosette Nebula, and qualitatively indicates that turbulent fluctuations in the Galactic field on spatial scales of $\sim 10$ pc are smaller than the mean Galactic field. Finally, our results show intriguing indications that some of the largest values of |RM| occur for lines of sight that pass outside the fully ionized shell of the IC 1805 HII region, but pass through the Photodissociation Region (PDR) associated with IC 1805.

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arXiv2016

VLA Measurements of Faraday Rotation through Coronal Mass Ejections

Coronal mass ejections (CMEs) are large-scale eruptions of plasma from the Sun that play an important role in space weather. Faraday rotation (FR) is the rotation of the plane of polarization that results when a linearly polarized signal passes through a magnetized plasma such as a CME. FR observations of a source near the Sun can provide information on the plasma structure of a CME shortly after launch. We report on simultaneous white-light and radio observations made of three CMEs in August 2012. We made sensitive Very Large Array (VLA) full-polarization observations using 1 - 2 GHz frequencies of a "constellation" of radio sources through the solar corona at heliocentric distances that ranged from 6 - 15 solar radii. Of the nine sources observed, three were occulted by CMEs: two sources (0842+1835 and 0900+1832) were occulted by a single CME and one source (0843+1547) was occulted by two CMEs. In addition to our radioastronomical observations, which represent one of the first active hunts for CME Faraday rotation since Bird et al. (1985) and the first active hunt using the VLA, we obtained white-light coronagraph images from the LASCO/C3 instrument to determine the Thomson scattering brightness, BT, providing a means to independently estimate the plasma density and determine its contribution to the observed Faraday rotation. A constant density force-free flux rope embedded in the background corona was used to model the effects of the CMEs on BT and FR. We demonstrate this model's ability to successfully reproduce both BT and FR profiles. The plasma densities (6 - 22 x 10$^3$ cm$^{-3}$) and axial magnetic field strengths (2 - 12 mG) inferred from our models are consistent with the modeling work of Liu et al. (2007) and Jensen & Russell (2008), as well as previous CME FR observations by Bird et al. (1985).

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arXiv2016

Denser Sampling of the Rosette Nebula with Faraday Rotation Measurements: Improved Estimates of Magnetic Fields in HII Regions

We report Faraday rotation measurements of 11 extragalactic radio sources with lines of sight through the Rosette Nebula, a prominent HII region associated with the star cluster NGC 2244. It is also a prototypical example of a "stellar bubble" produced by the winds of the stars in NGC 2244. The goal of these measurements is to better determine the strength and structure of the magnetic field in the nebula. We calculate the rotation measure (RM) through two methods, a least-squares fit to $χ$( $λ^2$) and Rotation Measure Synthesis. In conjunction with our results from Savage et al. (2013), we find an excess RM due to the shell of the nebula of +40 to +1200 rad m$^{-2}$ above a background RM of +147 rad m$^{-2}$. We discuss two forms of a simple shell model intended to reproduce the magnitude of the observed RM as a function of distance from the center of the Rosette Nebula. The models represent different physical situations for the magnetic field within the shell of the nebula. The first assumes that there is an increase in the magnetic field strength and plasma density at the outer radius of the HII region, such as would be produced by a strong magnetohydrodynamic shock wave. The second model assumes that any increase in the RM is due solely to an increase in the density, and the Galactic magnetic field is unaffected in the shell. We employ a Bayesian analysis to distinguish between the two forms of the model.

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arXiv2014

Measurements of Coronal Faraday Rotation at 4.6 Solar Radii

Many competing models for the coronal heating and acceleration mechanisms of the high-speed solar wind depend on the solar magnetic field and plasma structure in the corona within heliocentric distances of $5R_\odot$. We report on sensitive VLA full-polarization observations made in August, 2011, at 5.0 and 6.1 GHz (each with a bandwidth of 128 MHz) of the radio galaxy 3C228 through the solar corona at heliocentric distances of $4.6-5.0R_\odot$. Observations at 5.0 GHz permit measurements deeper in the corona than previous VLA observations at 1.4 and 1.7 GHz. These Faraday rotation observations provide unique information on the magnetic field in this region of the corona. The measured Faraday rotation on this day was lower than our a priori expectations, but we have successfully modeled the measurement in terms of observed properties of the corona on the day of observation. Our data on 3C228 provide two lines of sight (separated by 46'', 33,000 km in the corona). We detected three periods during which there appeared to be a difference in the Faraday rotation measure between these two closely spaced lines of sight. These measurements (termed differential Faraday rotation) yield an estimate of $2.6$ to $4.1$ GA for coronal currents. Our data also allow us to impose upper limits on rotation measure fluctuations caused by coronal waves; the observed upper limits were $3.3$ and $6.4$ rad/m$^2$ along the two lines of sight. The implications of these results for Joule heating and wave heating are briefly discussed.

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arXiv2013

Plasma Diagnostics of the Interstellar Medium with Radio Astronomy

We discuss the degree to which radio propagation measurements diagnose conditions in the ionized gas of the interstellar medium (ISM). The "signal generators" of the radio waves of interest are extragalactic radio sources (quasars and radio galaxies), as well as Galactic sources, primarily pulsars. The polarized synchrotron radiation of the Galactic non-thermal radiation also serves to probe the ISM, including space between the emitting regions and the solar system. Radio propagation measurements provide unique information on turbulence in the ISM as well as the mean plasma properties such as density and magnetic field strength. Radio propagation observations can provide input to the major contemporary questions on the nature of ISM turbulence, such as its dissipation mechanisms and the processes responsible for generating the turbulence on large spatial scales. Measurements of the large scale Galactic magnetic field via Faraday rotation provide unique observational input to theories of the generation of the Galactic field.

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arXiv2013

Probing the Rosette Nebula Stellar Bubble with Faraday Rotation

We report the results of Faraday rotation measurements of 23 background radio sources whose lines of sight pass through or close to the Rosette Nebula. The Rosette Nebula is an excellent candidate for studies of super bubbles associated with young star clusters. We made linear polarization measurements with the Karl G. Jansky Very Large Array (JVLA) at frequencies of 4.4GHz, 4.9GHz, and 7.7GHz. We are able to establish a background rotation measure in this part of the sky due to the Galaxy of +147 rad m^-2. Sources whose lines of sight pass through the nebula have an excess rotation measure of 50-750 rad m^-2, which we attribute to the plasma shell of the Rosette Nebula. We consider two simple plasma shell models and how they reproduce the magnitude and sign of the rotation measure, and its dependence on distance from the center of the nebula. These two models represent different modes of interaction of the Rosette Nebula star cluster with the surrounding interstellar medium. Both can reproduce the magnitude and spatial extent of the rotation measure enhancement, given plausible free parameters. We contend that the model based on a stellar bubble more closely reproduces the observed dependence of rotation measure on distance from the center of the nebula.

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arXiv2011

Properties of Turbulence in the Very Local Interstellar Clouds

We have investigated the degree to which turbulence in the Very Local Interstellar Clouds resembles the highly-studied turbulence in the solar corona and the solar wind. The turbulence diagnostics for the Local Clouds are the absorption line widths measured along 32 lines of sight to nearby stars, yielding measurements for 53 absorption components (Redfield and Linsky 2004). We have tested whether the Local Cloud turbulence has the following properties of turbulence in the solar corona or the solar wind: (a) velocity fluctuations mainly perpendicular to the average magnetic field, (b) a temperature anisotropy in the sense that the perpendicular temperature is larger than the parallel temperature (or at least enhanced relative to expectation), and (c) an ion temperature which is dependent on the ion Larmor radius, in the sense that more massive ions have higher temperatures. Our analysis of the data does not show compelling evidence for any of these properties in Local Cloud turbulence, indicating possible differences with heliospheric plasmas. In the case of anisotropy of velocity fluctuations, although the expected observational signature is not seen, we cannot exclude the possibility of relatively high degrees of anisotropy (anisotropy parameter $ε\sim 0.50 - 0.70$), if some other process in the the Local Clouds is causing variations in the turbulent line width from one line of sight to another. We briefly consider possible reasons for differences between coronal and solar wind turbulence and that in the Local Clouds.

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arXiv2010

Ion-Neutral Collisions in the Interstellar Medium: Wave Damping and Elimination of Collisionless Processes

Most phases of the interstellar medium contain neutral atoms in addition to ions and electrons. This introduces differences in plasma physics processes in those media relative to the solar corona and the solar wind at a heliocentric distance of 1 astronomical unit. In this paper, we consider two well-diagnosed, partially-ionized interstellar plasmas. The first is the Diffuse Ionized Gas (DIG) which is probably the extensive phase in terms of volume. The second is the gas that makes up the Local Clouds of the Very Local Interstellar Medium (VLISM). Ion-neutral interactions seem to be important in both media. In the DIG, ion-neutral collisions are relatively rare, but sufficiently frequent to damp magnetohydrodynamic (MHD) waves (as well as propagating MHD eddies) within less than a parsec of the site of generation. This result raises interesting questions about the sources of turbulence in the DIG. In the case of the VLISM, the ion-neutral collision frequency is higher than that in the DIG, because the hydrogen is partially neutral rather than fully ionized. We present results showing that prominent features of coronal and solar wind turbulence seem to be absent in VLISM turbulence. For example, ion temperature does not depend on ion mass. This difference may be attributable to ion-neutral collisions, which distribute power from more effectively heated massive ions such as iron to other ion species and neutral atoms.

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arXiv2010

Observational Tests of the Properties of Turbulence in the Very Local Interstellar Medium

The Very Local Interstellar Medium (VLISM) contains clouds which consist of partially-ionized plasma. These clouds can be effectively diagnosed via high resolution optical and ultraviolet spectroscopy of the absorption lines they form in the spectra of nearby stars. Among the information provided by these spectroscopic measurements are the root-mean-square velocity fluctuation due to turbulence in these clouds and the ion temperature, which may be partially determined by dissipation of turbulence. We consider whether this turbulence resembles the extensively studied and well-diagnosed turbulence in the solar wind and solar corona. Published observations are used to determine if the velocity fluctuations are primarily transverse to a large-scale magnetic field, whether the temperature perpendicular to the large scale field is larger than that parallel to the field, and whether ions with larger Larmor radii have higher temperatures than smaller gyroradius ions. Although a thorough investigation of the data is underway, a preliminary examination of the published data shows neither evidence for anisotropy of the velocity fluctuations or temperature, nor Larmor radius-dependent heating. These results indicate differences between solar wind and Local Cloud turbulence.

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arXiv2008

Joule Heating and Anomalous Resistivity in the Solar Corona

Recent radioastronomical observations of Faraday rotation in the solar corona can be interpreted as evidence for coronal currents, with values as large as $2.5 \times 10^9$ Amperes (Spangler 2007). These estimates of currents are used to develop a model for Joule heating in the corona. It is assumed that the currents are concentrated in thin current sheets, as suggested by theories of two dimensional magnetohydrodynamic turbulence. The Spitzer result for the resistivity is adopted as a lower limit to the true resistivity. The calculated volumetric heating rate is compared with an independent theoretical estimate by Cranmer et al (2007). This latter estimate accounts for the dynamic and thermodynamic properties of the corona at a heliocentric distance of several solar radii. Our calculated Joule heating rate is less than the Cranmer et al estimate by at least a factor of $3 \times 10^5$. The currents inferred from the observations of Spangler (2007) are not relevant to coronal heating unless the true resistivity is enormously increased relative to the Spitzer value. However, the same model for turbulent current sheets used to calculate the heating rate also gives an electron drift speed which can be comparable to the electron thermal speed, and larger than the ion acoustic speed. It is therefore possible that the coronal current sheets are unstable to current-driven instabilities which produce high levels of waves, enhance the resistivity and thus the heating rate.

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arXiv2008

Radio Remote Sensing of the Corona and the Solar Wind

Modern radio telescopes are extremely sensitive to plasma on the line of sight from a radio source to the antenna. Plasmas in the corona and solar wind produce measurable changes in the radio wave amplitude and phase, and the phase difference between wave fields of opposite circular polarization. Such measurements can be made of radio waves from spacecraft transmitters and extragalactic radio sources, using radio telescopes and spacecraft tracking antennas. Data have been taken at frequencies from about 80 MHz to 8000 MHz. Lower frequencies probe plasma at greater heliocentric distances. Analysis of these data yields information on the plasma density, density fluctuations, and plasma flow speeds in the corona and solar wind, and on the magnetic field in the solar corona. This paper will concentrate on the information that can be obtained from measurements of Faraday rotation through the corona and inner solar wind. The magnitude of Faraday rotation is proportional to the line of sight integral of the plasma density and the line-of-sight component of the magnetic field. Faraday rotation provides an almost unique means of estimating the magnetic field in this part of space. This technique has contributed to measurement of the large scale coronal magnetic field, the properties of electromagnetic turbulence in the corona, possible detection of electrical currents in the corona, and probing of the internal structure of coronal mass ejections (CMEs). This paper concentrates on the search for small-scale coronal turbulence and remote sensing of the structure of CMEs. Future investigations with the Expanded Very Large Array (EVLA) or Murchison Widefield Array (MWA) could provide unique observational input on the astrophysics of CMEs.

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