arXiv subjects

A. C. Birch

Publications and source records attributed to A. C. Birch.

At least 19 recordsLinked to original sources

arXiv2022

Impact of spatially correlated fluctuations in sunspots on metrics related to magnetic twist

The twist of the magnetic field above a sunspot is an important quantity in solar physics. For example, magnetic twist plays a role in the initiation of flares and coronal mass ejections (CMEs). Various proxies for the twist above the photosphere have been found using models of uniformly twisted flux tubes, and are routinely computed from single photospheric vector magnetograms. One class of proxies is based on $α_z$, the ratio of the vertical current to the vertical magnetic field. Another class of proxies is based on the so-called twist density, $q$, which depends on the ratio of the azimuthal field to the vertical field. However, the sensitivity of these proxies to temporal fluctuations of the magnetic field has not yet been well characterized. We aim to determine the sensitivity of twist proxies to temporal fluctuations in the magnetic field as estimated from time-series of SDO/HMI vector magnetic field maps. To this end, we introduce a model of a sunspot with a peak vertical field of 2370 Gauss at the photosphere and a uniform twist density $q= -0.024$ Mm$^{-1}$. We add realizations of the temporal fluctuations of the magnetic field that are consistent with SDO/HMI observations, including the spatial correlations. Using a Monte-Carlo approach, we determine the robustness of the different proxies to the temporal fluctuations. The temporal fluctuations of the three components of the magnetic field are correlated for spatial separations up to 1.4 Mm (more than expected from the point spread function alone). The Monte-Carlo approach enables us to demonstrate that several proxies for the twist of the magnetic field are not biased in each of the individual magnetograms. The associated random errors on the proxies have standard deviations in the range between $0.002$ and $0.006$ Mm$^{-1}$, which is smaller by approximately one order of magnitude than the mean value of $q$.

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arXiv2021

Evolution of solar surface inflows around emerging active regions

Solar active regions are associated with Evershed outflows in sunspot penumbrae, moat outflows surrounding sunspots, and extended inflows surrounding active regions. The latter have been identified on established active regions by various methods. The evolution of these inflows and their dependence on active region properties as well as their impact on the global magnetic field are not yet understood. We aim to understand the evolution of the average inflows around emerging active regions and to derive an empirical model for these inflows. We analyze horizontal flows at the surface of the Sun using local correlation tracking of solar granules observed in continuum images of SDO/HMI. We measure average flows of a sample of 182 isolated active regions up to seven days before and after their emergence onto the solar surface with a cadence of 12 hours. We investigate the average inflow properties with respect to active region characteristics of total flux and latitude. We fit a model to these observed inflows for a quantitative analysis. We find that converging flows of around $20$ to $30$ m/s are first visible one day prior to emergence, in agreement with recent results. These converging flows are present independently of active region properties of latitude or flux. We confirm a recently found prograde flow of about $40$ m/s at the leading polarity during emergence. We find that the time after emergence when the latitudinal inflows increase in amplitude depends on the flux of the active region, ranging from one to four days after emergence and increasing with flux. The largest extent of the inflows is up to about $7 \pm 1^\circ$ away from the center of the active region within the first six days after emergence. The inflow velocities have amplitudes of about $50$ m/s.

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arXiv2021

Probing the Solar Meridional Circulation using Fourier Legendre Decomposition

We apply the helioseismic methodology of Legendre Function Decomposition to 88 months of Dopplergrams obtained by the Helioseismic and Magnetic Imager (HMI) as the basis of inferring the depth variation of the mean meridional flow, as averaged between 20 and 60 degrees latitude and in time, in both the northern and southern hemispheres. We develop and apply control procedures designed to assess and remove center-to-limb artifacts, using measurements obtained by performing the analysis with respect to artificial poles at the east and west limbs. Forward modeling is carried out, using sensitivity functions proportional to the mode kinetic energy density, to evaluate the consistency of the corrected frequency shifts with models of the depth variation of the meridional circulation in the top half of the convection zone. The results, taken at face value, imply substantial differences between the meridional circulation in the northern and southern hemisphere. The inferred presence of a return (equator-ward propagating) flow at a depth of approximately 40 Mm below the photosphere in the northern hemisphere is surprising and appears to be inconsistent with many other helioseismic analyses. This discrepancy may be the result of an inadequacy of our methodology to remove systematic errors in HMI data. Our results appear to be at least qualitative similar to those by Gizon et al. (2020) which point to an anomaly in HMI data that is not present in MDI or GONG data.

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arXiv2020

Predicting frequency changes of global-scale solar Rossby modes due to solar cycle changes in internal rotation

Context. Large-scale equatorial Rossby modes have been observed on the Sun over the last two solar cycles. Aims. We investigate the impact of the time-varying zonal flows on the frequencies of Rossby modes. Methods. A first-order perturbation theory approach is used to obtain an expression for the expected shift in the mode frequencies due to perturbations in the internal rotation rate. Results. Using the time-varying rotation from helioseismic inversions we predict the changes in Rossby mode frequencies with azimuthal orders from m = 1 to m = 15 over the last two solar cycles. The peak-to-peak frequency change is less than 1 nHz for the m = 1 mode, grows with m, and reaches 25 nHz for m = 15. Conclusions. Given the observational uncertainties on mode frequencies due to the finite mode lifetimes, we find that the predicted frequency shifts are near the limit of detectability.

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arXiv2020

Estimating the nonstructural component of the helioseismic surface term using hydrodynamic simulations

As the amount of asteroseismic data available continues to grow, the inability to accurately model observed oscillation frequencies is becoming a critical problem for interpreting these frequencies. A major component of this problem is the modeling of the near-surface layers. Our aim is to develop a method to estimate the effect of the near-surface layers on oscillation frequencies. In the proposed method we numerically estimate eigenfunctions in 3D hydrodynamic simulations. We match those to the eigenfunctions calculated from the classic equations applied to the horizontal averages of the structure variables. We use this procedure to calculate the frequency perturbation resulting from the dynamical part of the interaction of the oscillations with near-surface convection. As the last step we scale the numbers to the Sun. To provide a qualitative test of our method we performed a series of simulations, calculated the perturbations using our procedure, and compared them to previously reported residuals relative to solar models. We find that we can largely reproduce the observed frequency residuals without resorting to poorly justified theoretical models. We find that, while the calculations of Houdek et al. (2017, MNRAS, 464, L124) produce similar frequency perturbations, the density-pressure phase differences computed here do not match those of that work.

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arXiv2020

Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation

Large-scale Rossby waves have recently been discovered from measurements of horizontal surface and near-surface solar flows (Löptien at al. 2018). We are interested in understanding why only the sectoral modes are seen in the observations and also in modelling the radial structure of the observed modes. To do so, we characterise here the radial eigenfunctions of r modes for slowly-rotating polytropes in uniform rotation. We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density, r modes can only exist for $\ell=m$ spherical harmonics in the inviscid case, and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales as $r^m$. For all r modes except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance. The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the statement that the system needs to be in both horizontal and radial force balance. In the absence of super- or subadiabatic stratification and viscosity, both the horizontal and radial force balances independently determine the pressure perturbation. The only quasi-toroidal cases in which the two determinations of the pressure perturbation are consistent are the special cases where $\ell=m$, and the horizontal displacement scales with $r^m$.

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arXiv2020

Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis

Global-scale Rossby waves have recently been unambiguously identified on the Sun. Here we study the latitude and depth dependence of the Rossby wave eigenfunctions. By applying helioseismic ring-diagram analysis and granulation tracking to SDO/HMI observations, we compute maps of the radial vorticity of flows in the upper solar convection zone (down to depths of more than $16$ Mm). We use a Fourier transform in longitude to separate the different azimuthal orders m in the range $3 \le m \le 15$. At each $m$ we obtain the phase and amplitude of the Rossby waves as a function of depth using the helioseismic data. At each $m$ we also measure the latitude dependence of the eigenfunctions by calculating the covariance between the equator and other latitudes. We then study the horizontal and radial dependences of the radial vorticity eigenfunctions. The horizontal eigenfunctions are complex. As observed previously, the real part peaks at the equator and switches sign near $\pm 30^\circ$, thus the eigenfunctions show significant non-sectoral contributions. The imaginary part is smaller than the real part. The phase of the radial eigenfunctions varies by only roughly $\pm 5^\circ$ over the top $15$ Mm. The amplitude of the radial eigenfunctions decreases by about $10\%$ from the surface down to $8$ Mm (the region where ring-diagram analysis is most reliable, as seen by comparing with the rotation rate measured by global-mode seismology). The radial dependence of the radial vorticity eigenfunctions deduced from ring-diagram analysis is consistent with a power-law down to $8$ Mm and is unreliable at larger depths. However, the observations provide only weak constraints on the power-law exponents. For the real part, the latitude dependence of the eigenfunctions is consistent with previous work (using granulation tracking). The imaginary part is smaller than the real part but significantly nonzero.

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arXiv2018

Validating Forward Modeling and Inversions of Helioseismic Holography Measurements

Here we use synthetic data to explore the performance of forward models and inverse methods for helioseismic holography. Specifically, this work presents the first comprehensive test of inverse modeling for flows using lateral-vantage (deep-focus) holography. We derive sensitivity functions in the Born approximation. We then use these sensitivity functions in a series of forward models and inversions of flows from a publicly available magnetohydrodynamic quiet-Sun simulation. The forward travel times computed using the kernels generally compare favorably with measurements obtained by applying holography, in a lateral-vantage configuration, on a 15-hour time series of artificial Dopplergrams extracted from the simulation. Inversions for the horizontal flow components are able to reproduce the flows in the upper 3Mm of the domain, but are compromised by noise at greater depths.

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arXiv2018

Evolution and wave-like properties of the average solar supergranule

Solar supergranulation presents us with many mysteries. For example, previous studies in spectral space found that supergranulation has wave-like properties. Here we study, in real space, the wave-like evolution of the average supergranule over a range of spatial scales (from 10 to 80 Mm). We complement this by characterizing the evolution of the associated network magnetic field. We use one year of data from the Helioseismic and Magnetic Imager (HMI) to measure horizontal near-surface flows near the solar equator by applying time-distance helioseismology on Dopplergrams and granulation tracking on intensity images. The average supergranule outflow (or inflow) is constructed by averaging over 10000 individual outflows (or inflows). The contemporaneous evolution of the magnetic field is studied with HMI line-of-sight observations. We confirm and extend previous measurements of the supergranular wave dispersion relation to angular wavenumbers in the range 50 120. In real space, larger supergranules undergo oscillations with longer periods and lifetimes than smaller cells. We find excellent agreement between TD and LCT and obtain wave properties that are independent of the tracking rate. The observed network magnetic field follows the oscillations of the supergranular flows with a six-hour time lag. This behavior can be explained by computing the motions of corks carried by the supergranular flows. Signatures of supergranular waves in surface horizontal flows near the solar equator can be observed in real space. These oscillatory flows control the evolution of the network magnetic field, in particular they explain the recently discovered east-west anisotropy of the magnetic field around the average supergranule. Background flow measurements that we obtain from Doppler frequency shifts do not favor shallow models of supergranulation.

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arXiv2017

Helioseismic Holography of Simulated Sunspots: dependence of the travel time on magnetic field strength and Wilson depression

Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-time shifts at frequencies above approximately 3.50 mHz (depending on the phase-speed filter) are insensitive to the magnetic field strength. The travel time of these waves is determined exclusively by the Wilson depression and sound-speed perturbation. The travel time of waves with lower frequencies is affected by the direct effect of the magnetic field, although photospheric field strengths below 1500 G do not leave a significant trace on the travel-time measurements. These results could potentially be used to develop simplified travel-time inversion methods.

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arXiv2017

Measuring solar active region inflows with local correlation tracking of granulation

Context. Local helioseismology has detected spatially extended converging surface flows into solar active regions. These play an important role in flux-transport models of the solar dynamo. Aims. We aim to validate the existence of the inflows by deriving horizontal flow velocities around active regions with local correlation tracking of granulation. Methods. We generate a six-year long-time series of full-disk maps of the horizontal velocity at the solar surface by tracking granules in continuum intensity images provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Results. On average, active regions are surrounded by inflows extending up to 10 deg from the center of the active region of magnitudes of 20-30 m/s, reaching locally up to 40 m/s, which is in agreement with results from local helioseismology. By computing an ensemble average consisting of 243 individual active regions, we show that the inflows are not azimuthally symmetric but converge predominantly towards the trailing polarity of the active region with respect to the longitudinally and temporally averaged flow field.

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arXiv2016

Intensity contrast of the average supergranule

While the velocity fluctuations of supergranulation dominate the spectrum of solar convection at the solar surface, very little is known about the fluctuations in other physical quantities like temperature or density at supergranulation scale. Using SDO/HMI observations, we characterize the intensity contrast of solar supergranulation at the solar surface. We identify the positions of ${\sim}10^4$ outflow and inflow regions at supergranulation scales, from which we construct average flow maps and co-aligned intensity and magnetic field maps. In the average outflow center, the maximum intensity contrast is $(7.8\pm0.6)\times10^{-4}$ (there is no corresponding feature in the line-of-sight magnetic field). This corresponds to a temperature perturbation of about $1.1\pm0.1$ K, in agreement with previous studies. We discover an east-west anisotropy, with a slightly deeper intensity minimum east of the outflow center. The evolution is asymmetric in time: the intensity excess is larger 8 hours before the reference time (the time of maximum outflow), while it has almost disappeared 8 hours after the reference time. In the average inflow region, the intensity contrast mostly follows the magnetic field distribution, except for an east-west anisotropic component that dominates 8 hours before the reference time. We suggest that the east-west anisotropy in the intensity is related to the wave-like properties of supergranulation.

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arXiv2016

SDO/HMI survey of emerging active regions for helioseismology

Observations from the Solar Dynamics Observatory (SDO) have the potential for allowing the helioseismic study of the formation of hundreds of active regions, which would enable us to perform statistical analyses. Our goal is to collate a uniform data set of emerging active regions observed by the SDO/HMI instrument suitable for helioseismic analysis up to seven days before emergence. We restricted the sample to active regions that were visible in the continuum and emerged into quiet Sun largely avoiding pre-existing magnetic regions. As a reference data set we paired a control region (CR), with the same latitude and distance from central meridian, with each emerging active region (EAR). We call this data set, which is currently comprised of 105 emerging active regions observed between May 2010 and November 2012, the SDO Helioseismic Emerging Active Region (SDO/HEAR) survey. To demonstrate the utility of a data set of a large number of emerging active regions, we measure the relative east-west velocity of the leading and trailing polarities from the line-of-sight magnetogram maps during the first day after emergence. The latitudinally averaged line-of-sight magnetic field of all the EARs shows that, on average, the leading (trailing) polarity moves in a prograde (retrograde) direction with a speed of 121 +/- 22 m/s (-70 +/- 13 m/s) relative to the Carrington rotation rate in the first day. However, relative to the differential rotation of the surface plasma, the east-west velocity is symmetric, with a mean of 95 +/- 13 m/s. The SDO/HEAR data set will not only be useful for helioseismic studies, but will also be useful to study other features such as the surface magnetic field evolution of a large sample of EARs.

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arXiv2016

Helioseismic holography of simulated sunspots: magnetic and thermal contributions to travel times

Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path towards inversions for sunspot structure.

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arXiv2016

The shrinking Sun: a systematic error in local correlation tracking of solar granulation

Context. Local correlation tracking of granulation (LCT) is an important method for measuring horizontal flows in the photosphere. This method exhibits a systematic error that looks like a flow converging towards disk center, also known as the shrinking-Sun effect. Aims. We aim at studying the nature of the shrinking-Sun effect for continuum intensity data and at deriving a simple model that can explain its origin. Methods. We derived LCT flow maps by running the local correlation tracking code FLCT on tracked and remapped continuum intensity maps provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We also computed flow maps from synthetic continuum images generated from STAGGER code simulations of solar surface convection. We investigated the origin of the shrinking-Sun effect by generating an average granule from synthetic data from the simulations. Results. The LCT flow maps derived from HMI and from the simulations exhibit a shrinking-Sun effect of comparable magnitude. The origin of this effect is related to the apparent asymmetry of granulation originating from radiative transfer effects when observing with a viewing angle inclined from vertical. This causes, in combination with the expansion of the granules, an apparent motion towards disk center.

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arXiv2015

Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking

Flow vorticity is a fundamental property of turbulent convection in rotating systems. Solar supergranules exhibit a preferred sense of rotation, which depends on the hemisphere. This is due to the Coriolis force acting on the diverging horizontal flows. We aim to spatially resolve the vertical flow vorticity of the average supergranule at different latitudes, both for outflow and inflow regions. To measure the vertical vorticity, we use two independent techniques: time-distance helioseismology (TD) and local correlation tracking of granules in intensity images (LCT) using data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Both maps are corrected for center-to-limb systematic errors. We find that 8-h TD and LCT maps of vertical vorticity are highly correlated at large spatial scales. Associated with the average supergranule outflow, we find tangential (vortical) flows that reach about 10 m/s in the clockwise direction at 40° latitude. In average inflow regions, the tangential flow reaches the same magnitude, but in the anti-clockwise direction. These tangential velocities are much smaller than the radial (diverging) flow component (300 m/s for the average outflow and 200 m/s for the average inflow). The results for TD and LCT as measured from HMI are in excellent agreement for latitudes between $-$60° and 60°. From HMI LCT, we measure the vorticity peak of the average supergranule to have a full width at half maximum of about 13 Mm for outflows and 8 Mm for inflows. This is larger than the spatial resolution of the LCT measurements (about 3 Mm). On the other hand, the vorticity peak in outflows is about half the value measured at inflows (e.g. 4/(10^6 s) clockwise compared to 8/(10^6 s) anti-clockwise at 40° latitude). Results from MDI/SOHO obtained in 2010 are biased compared to the HMI/SDO results for the same period.

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arXiv2015

Anisotropy of the solar network magnetic field around the average supergranule

Supergranules in the quiet Sun are outlined by a web-like structure of enhanced magnetic field strength, the so-called magnetic network. We aim to map the magnetic network field around the average supergranule near disk center. We use observations of the line-of-sight component of the magnetic field from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The average supergranule is constructed by coaligning and averaging over 3000 individual supergranules. We determine the positions of the supergranules with an image segmentation algorithm that we apply on maps of the horizontal flow divergence measured using time-distance helioseismology. In the center of the average supergranule the magnetic (intranetwork) field is weaker by about 2.2 Gauss than the background value (3.5 Gauss), whereas it is enhanced in the surrounding ring of horizontal inflows (by about 0.6 Gauss on average). We find that this network field is significantly stronger west (prograde) of the average supergranule than in the east (by about 0.3 Gauss). With time-distance helioseismology, we find a similar anisotropy. The observed anisotropy of the magnetic field adds to the mysterious dynamical properties of solar supergranulation.

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arXiv2014

Evaluation of the capability of local helioseismology to discern between monolithic and spaghetti sunspot models

The helioseismic properties of the wave scattering generated by monolithic and spaghetti sunspots are analyzed by means of numerical simulations. In these computations, an incident f or p1 mode travels through the sunspot model, which produces absorption and phase shift of the waves. The scattering is studied by inspecting the wavefield, computing travel-time shifts, and performing Fourier-Hankel analysis. The comparison between the results obtained for both sunspot models reveals that the differences in the absorption coefficient can be detected above noise level. The spaghetti model produces an steep increase of the phase shift with the degree of the mode at short wavelengths, while mode-mixing is more efficient for the monolithic model. These results provide a clue for what to look for in solar observations to discern the constitution of sunspots between the proposed monolithic and spaghetti models.

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