Draft version November 14, 2013 Preprint typeset using LATEX style emulateapj v. 04/17/13
FIRST DETECTION OF THERMAL RADIO EMISSION FROM SOLAR-TYPE STARS WITH THE JANSKY VLA Jackie Villadsen, Gregg Hallinan, Stephen Bourke Astronomy Department, California Institute of Technology, Pasadena, CA 91125 Draft version November 14, 2013
ABSTRACT We present the first detections of thermal radio emission from the atmospheres of solar-type stars τ Cet, η Cas A, and 40 Eri A. These stars all resemble the Sun in age and level of magnetic activity, as indicated by X-ray luminosity and chromospheric emission in calcium H and K lines. We observed these stars with the Jansky VLA with sensitivities of a few µJy at combinations of 10.0, 15.0, and 34.5 GHz. τ Cet, η Cas A, and 40 Eri A are all detected at 34.5 GHz with signal-to-noise ratios of 7.6, 4.6, and 4.2, respectively. 15.0-GHz upper limits imply a rising spectral index greater than 1.0 for τ Cet and 1.7 for η Cas A, at the 99% confidence level. The measured 34.5-GHz fluxes correspond to stellar disk-averaged brightness temperatures of roughly 10,000 K, similar to the solar brightness temperature at the same frequency. We explain this emission as optically-thick thermal free-free emission from the chromosphere, with possible contributions from coronal gyroresonance emission above active regions and coronal free-free emission.
1. INTRODUCTION a radio luminosity roughly 10 times that of the quiet Efforts to measure radio emission from the Sun started Sun due to its larger surface area and somewhat higher as early as 1896 [Wilsing & Scheiner (1896)]. The first brightness temperature. detections occurred during the boom in radio technology In low-mass main-sequence stars, the only form of development during World War II, when military radio quiescent radio emission as of yet detected is gyrosyn- engineers James Stanley Hey (1946) in Britain, George chrotron emission from a persistent non-thermal corona, Clark Southworth (1945) in the United States, and Bruce a feature which has no analog in the Sun. G¨udelet al. Slee in Australia (Orchiston (2005)) all independently (1994) reported the detection of 8.5-GHz emission from identified solar radio emission as a source of interference solar-type stars, with radio luminosities a few thousand in their radar signals. times that of the Sun. These stars also have X-ray lu- Seventy years later, solar radio observations have con- minosities much higher than the Sun, following an X- tributed significantly to a detailed (although far from ray-radio luminosity relation observed by G¨udel& Benz complete) understanding of the solar atmosphere. So- (1993) in quiescent emission from coronae of active stars lar flares produce transient radio emission from MHz to with spectral type F to M. Benz & G¨udel(1994) ob- GHz frequencies, including gyrosynchrotron storms and served that the X-ray-radio luminosity relation is also coherent bursts, which act as diagnostics of electron den- seen in solar flares, suggesting that non-thermal stellar sity and magnetic field strength in the solar corona (see radio “coronae” may consist of the emission from many Bastian et al. (1998) for a review). small flares, or at least are continuously heated by flares. The microwave emission from the quiet Sun consists Previous to the results reported here, the most sen- of thermal radiation from the chromosphere at ∼ 104 K, sitive microwave observations of solar-type stars with which is optically thick at microwave frequencies due to solar-like X-ray luminosities were performed with the free-free opacity. The quiet-Sun brightness temperature Very Large Array (VLA) by G¨udel (1992), placing a 3- sigma upper limit of 80 µJy on the 8.3-GHz flux of 40 spectrum probes atmospheric temperature and density 1 from the temperature minimum (far-IR) to the upper Eridani A. With the enhanced sensitivity of the Jansky chromosphere (cm wavelengths), as modeled in Louk- VLA, the observations described in this paper reached a itcheva et al. (2004). During periods of heightened solar 3-sigma detection limit of 6 to 12 µJy in a few hours of activity, low-frequency solar radiation (below 10-20 GHz) observation, enabling the first detections of microwave is enhanced by bright spots above active regions, where radio emission from the thermal atmospheres of solar- the ∼ 106-K corona is optically thick to gyroresonant type stars. and/or free-free opacity. For this reason, the 10.7-cm so- In this paper we present the first detections of ther- mal radio emission from three nearby solar-type stars lar flux F10.7 is a traditional measure of solar activity, varying by a factor of 2 to 3 during the solar cycle. with solar-like levels of magnetic activity: τ Ceti, η Cas- Radio luminosities at the level of the quiet Sun have yet siopeiae A, and 40 Eridani A. In Section 2, we review to be detected in other cool main-sequence stars because basic stellar parameters and activity indicators of our of the low fluxes: a few tens of µJy or less for stars at a sample, describe the observing program, and discuss the few parsecs. Just beyond the main sequence, Drake et al. (1993) detected 8.3-GHz thermal chromospheric emission 1 In contrast, these stars are easily detected at sub-mm wave- lengths, where the optically-thick thermal emission from the low from Procyon, a slightly-evolved F5 subgiant, which has chromosphere is of order a few mJy, and which must be accounted for in sub-mm observations of debris disks, as for τ Cet in Greaves [email protected] et al. (2004). 2
Name HD Distance (pc) Spectral Type Mass (M ) Radius (R ) Teff (K) [Fe/H] Known Stellar Companions τ Cet 10700 3.65 a G8.5V b 0.783 c 0.790 d 5400 b -0.40 b none η Cas A 4614 5.95 a F9V e 0.972 f 1.039 f 6000 f -0.25 g K7V @ 70 AU (12”) h 40 Eri A 26965 4.98 a K0.5V b 0.84 i 0.77 j 5100 b -0.28 b DA3 & M5Ve @ 400 AU (80”) k Sun — 4.8e-6 G2V 1 1 5700 0 none aBased on stellar parallaxes from van Leeuwen (2007). bGray et al. (2006). cTeixeira et al. (2009). ddi Folco et al. (2007). eGray et al. (2001b). fBoyajian et al. (2012). gGray et al. (2001a). hMason et al. (2013). The distances of stellar companions are reported as the orbital semi-major axis. iHolmberg et al. (2007). jDemory et al. (2009). kHeintz (1974).
TABLE 1 Basic stellar properties. probability of chance alignment of extragalactic sources. from the National Radio Astronomy Observatory’s Very Section 3 presents the source detections at various fre- Large Array (VLA) at latitude 34.1◦ N: τ Cet, η Cas A, quencies, draws a comparison to the solar spectrum, and 40 Eri A. Tables 1 and 2 compare these stars’ prop- and considers possible causes for a discrepancy in ra- erties, including a number of measures of stellar activity, dio and optical source coordinates. Section 4 discusses to those of the Sun. All three stars are a good match for the various possible radio emission mechanisms for the the Sun in age and activity level. detected sources: chromospheric disk emission, gyrores- onance emission above active regions, free-free emission 2.2. List of Observations from the corona and stellar wind, gyrosynchrotron emis- Table 3 summarizes the observations of all stars in the sion from a non-thermal corona, or flare emission. In sample. Each star in the sample was observed with some Section 5, we conclude with a review of the detected subset of X band (8.0 - 12.0 GHz), Ku band (12.0 - 18.0 sources and most likely emission mechanisms, and dis- GHz), and Ka band (tuned to 30.5 - 38.5 GHz). The cuss the potential for future observations with the VLA, VLA WIDAR correlator’s 3-bit observing mode enabled ALMA, and the SKA. up to 8-GHz bandwidth. Observations were performed between March and September 2013, with the VLA in 2. OBSERVATIONS D array and C array as well as intermediate configura- 2.1. Sample tions. Observations alternated between a nearby phase Our sample consists of three of the nearest stars of calibrator and the target source with cycle times of 7.5 spectral type F9V through K0.5V that are observable minutes in Ka band and 17 minutes in X and Ku band. Typical sensitivities obtained with the full bandwidth in Name log L P (days) log R0 Age (Gyr) 10 X rot 10 HK one hour were 4, 5, and 9 µJy in X, Ku, and Ka bands, (erg/s) respectively. τ Cet 26.5 a 34 b -5.01 c 5.8 d η Cas A 27.4 a 14.96 e -4.93 c 2.9 d 2.3. Source Motion 40 Eri A 27.2 a 43 b -4.872 b 5.6 d The expected positions of the sources were determined Sun 27.35 f 26.1 g -4.906 d 4.6 h using Hipparcos coordinates and proper motions (van Leeuwen (2007)), with an additional correction for par- TABLE 2 allactic motion based on the distances in Table 1. In Measures of stellar magnetic activity. addition, the position of η Cas A was corrected for dis- placement due to orbital acceleration, which resulted in aStellar X-ray luminosities are from pointed observations by the a 0.3” displacement northwest of the position expected ROSAT High-Resolution Imager (HRI) as reported by Schmitt & Liefke (2004) in the NEXXUS catalog. from proper motion and parallax. The orbital ephemeris bBaliunas et al. (1996). Determined from rotational modulation calculation used the US Naval Observatory’s Washington of Ca-II H&K lines. Double Star Catalog by Mason et al. (2013). 40 Eri A cCanto Martins et al. (2011) did not require a correction for orbital motion because dMamajek & Hillenbrand (2008). Note that age is not an indepen- the 40 Eri orbital period is much longer than that of η dent measure of activity: these ages were derived using empirical gyrochronology relations from rotation rates, which were in turn Cas. 0 Since the targets are within a few parsecs, the sources derived from log10 RHK. eL´opez-Santiago et al. (2010). “Photometric period found in the moved by as much as 1” due to proper motion and par- literature.” allax during the half-year in which we observed. In com- f Judge et al. (2003). The solar LX is an average value over the parison, our Ka-band observations reached a typical syn- solar cycle, calculated for the ROSAT All-Sky Survey 0.1 to 2.4 keV thesized beam of 1” and an astrometric accuracy of or- bandpass. The solar LX varies by about an order of magnitude from solar minimum to solar maximum. der 0.1”. To avoid smearing of the source and obtain gDonahue et al. (1996) accurate astrometry, we used the interferometry soft- hBouvier & Wadhwa (2010) ware package CASA’s routine fixvis to shift the visibility 3
Star Band Center Band- # of Epochsa Duration VLA Con- Beam Dimensionsb RMS Frequency width (h) figuration (µJy) (GHz) (GHz) τ Cet Ka 34.5 8.0 2 5.0 DnC 2.11” × 1.45” 3.9 Ku 15.0 6.0 1 2.0 D 8.99” × 4.64” 3.0 η Cas A Ka 34.5 8.0 4 8.0 DnC/C 1.01” × 0.83” 3.1 Ku 15.0 6.0 3 5.0 D/C 2.40” × 2.25” 2.1 X 10.0 4.0 2 3.0 D 11.93” × 7.98” 2.7 40 Eri A Ka 34.5 8.0 3 5.5 DnC→C/C 0.98” × 0.73” 3.7 aAll observations were made between March and September 2013. bMajor axis FWHM × minor axis FWHM.
TABLE 3 Summary of observations. phases to keep the source at the phase center in all ob- intensity). We used the Stokes V (circularly polarized) servations, before combining and imaging visibility data flux at the pixel representing the expected position of the from different epochs. source to calculate confidence intervals on the degree of circular polarization rc = V/I for each source, where rc 2.4. Chance Alignment of Extragalactic Sources varies from -1 to 1. We obtained 95%-confidence intervals Based on the 3-GHz source count of Condon et al. on rc of [-0.43,0.12], [-0.21,0.77], and [-0.89,0.13] for τ (2012), chance alignment of an unrelated source is a neg- Cet, η Cas A, and 40 Eri A, respectively. Thus, all of our ligible source of error in these observations. Condon et al. observations are consisent with zero circular polarization. (2012) performed 3-GHz source counts with 1-µJy sensi- tivity and measured a differential source count of: 3.1.1. Positions n(S) = 9000S−1.7 Jy−1 sr−1 (1) The last column of Table 4 shows the offset of the VLA- observed position of each source compared to the phase Considering the worse case scenario where source center, which is the expected position predicted from counts are independent of frequency, then the highest Hipparcos coordinates and proper motions, as described probability of finding a 1-sigma unrelated source within in Section 2.3. This offset is given in units of sigma, i.e. the synthesized beam is 18%, for the X-band observations the offset distance in arcseconds divided by the ampli- of η Cas A (since those observations have the largest syn- tude of the position error ellipse in arcseconds in the off- thesized beam). For most other observations, the prob- set direction. The position error ellipse is the synthesized ability is much lower. In all cases where a source was beam, defined as the CLEAN restoring beam, divided by detected, the probability of an unrelated source with flux the signal-to-noise ratio of the source detection. η Cas greater than or equal to the detected level (see Table 4) A and 40 Eri A show good agreement between the ex- falling in the synthesized beam is 0.1% or less. In addi- pected and observed positions. τ Cet shows a 3.8-sigma, tion, most extragalactic sources have a falling spectrum or 3.6”, difference; however, the expected position agrees at GHz frequencies, so the probabilities of chance align- well with the location of peak flux. We are confident that ment of detectable sources in the observed bands (10, 15, the observed source is indeed τ Cet, because of the low and 34.5 GHz) are significantly lower than at 3 GHz. probability of coincidence of an extragalactic source, and because the observed source is the only source detected 3. RESULTS in the 1.3’ primary beam at the 4-sigma level or greater. 3.1. Detections Solar-type stars τ Cet, η Cas A, and 40 Eri A were all 3.2. Brightness Temperature Spectra detected in Ka band (center frequency 34.5 GHz) with Figure 2 shows our constraints on the brightness tem- signal-to-noise ratio (SNR) of 7.6, 4.6, and 4.2, respec- perature (Tb) spectra of the observed stars, compared to tively. Table 4 gives the measured flux for each source, the solar Tb spectrum. All three detections of solar-type where all the Ka-band observations of a single source from different dates have been combined. Figure 1 shows Star 34.5-GHz RMS SNR Position Brightness the VLA images of the detections (also one image per Flux (µJy) Offset Temperature a star, with all Ka-band observations combined). Fluxes (µJy) (sigma) (K)b and source positions were determined by using CASA’s τ Cet 29.7 3.9 7.6 3.8 10900±1400 imfit task to fit an elliptical Gaussian to the source in η Cas A 14.4 3.1 4.6 1.3 8600±1800 the CLEAN image, with the constraint that the elliptical 40 Eri A 15.7 3.7 4.2 0.8 9700±2300 Gaussian have the dimensions of the CLEAN restoring TABLE 4 beam (i.e. assuming that the source is a point source). Detections. To check whether the source was consistent with a point source, imfit was also used to fit an elliptical Gaussian with unconstrained shape, which yielded dimensions con- aThe offset from the expected position based on Hipparcos as- trometry [van Leeuwen (2007)], in units of sigma (i.e. the distance sistent with the CLEAN beam to within 3 sigma for all between the measured and expected coords, divided by the ampli- sources. tude of the error ellipse in the offset direction). The sources were imaged in full Stokes, but were only bBrightness temperature is averaged over the stellar disk, using detected at or above the 3-sigma level in Stokes I (total the photospheric radii and distances reported in Table 1. 4
stars are consistent with the solar brightness tempera- ture in Ka band, suggesting that the emission observed in these cases is most likely chromospheric blackbody emission as in the Sun (see Section 4.1). The upper lim- its placed on the stars’ Tb are all consistent with the solar brightness temperature spectrum, as well.
3.2.1. Spectral Index The combination of the upper limits on 15.0-GHz flux and the measured 34.5-GHz fluxes indicates that τ Cet and η Cas A have rising spectra from 15.0 to 34.5 GHz. We calculated lower limits on the 15-to-34.5-GHz spec- tral index α for these two stars. To do so, we considered the measured value for the Ku-band flux to be the Ku- band flux in the pixel at the star’s known location (4.6 µJy for τ Cet and -5.6 µJy for η Cas A), drawn from a Gaussian distribution with the image RMS. The poste- rior probability distribution for spectral index was cal- culated using least-informative Jeffreys priors, resulting in 95%-confidence lower limits on α of 1.3 and 2.3, for τ Cet and η Cas A, respectively, and 99%-confidence lower limits of 1.0 and 1.7.
4. INTERPRETATION This section reviews the various sources of solar and stellar radio emission, focusing on quiescent emission, and assesses which sources may contribute to the de- tected 34.5-GHz emission from τ Cet, η Cas A, and 40 Eri A.
4.1. Chromospheric stellar disk emission 1. 35-GHz solar radio emission is dominated by ther- mal emission from the chromosphere, which is opti- cally thick at cm wavelengths due to free-free opac- ity.
2. The disk-averaged brightness temperatures re- ported in Table 4 are consistent with the 35-GHz quiet-Sun brightness temperature of 9300 K re- ported in White (2004).
3. Section 4.2 argues that the contribution to the emission from coronal bright spots above active re- gions is minimal.
4. paragraph about how to constrain temperature and density profiles of the solar atmosphere from the brightness temperature spectrum
(a) At microwave frequencies, the radio opacity of the quiet Sun is dominated by free-free opacity from free electrons and ions. (b) Equation 20 in Dulk (1985) gives an expres- sion for the free-free absorption coefficient for thermal electrons over a range of tempera- tures and densities. At a mid-chromospheric temperature of 104 K and a frequency near 34.5 GHz, the expression simplifies to: Fig. 1.— The above images show the Ka-band detections of the stars. The x- and y-axis are labelled with offset in arcseconds in (c) eqn for free-free absorption coefficient the E-W and N-S directions, respectively. The red cross shows the location of the star, determined from Hipparcos astrometry [van (d) The brightness temperature spectrum gives Leeuwen (2007)] and adjusted for proper motion, parallax, and (for the average temperature of a layer of the chro- η Cas A) orbital motion, to the epoch of the observations. The size of the cross marker is arbitrary, because the errors on astrometry, mosphere near optical depth of unity. of order 0.1 arcsec, are too small to show in these images. See Section 3.1.1 for a comparison of Hipparcos positions and observed positions. 5
(e) A brightness temperature spectrum covering a wide range of frequencies can constrain tem- perature and density profiles of model chro- mospheres, as for models of the solar chro- mosphere in Loukitcheva et al. (2004) and Fontenla et al. (2007).
4.2. Coronal emission above active regions 1. The enhanced densities and magnetic field strengths above active regions may cause the corona to become optically thick due to free-free or gyroresonant opacity, resulting in bright spots at coronal temperatures of ∼ 106 K on the 104-K stellar disk. 2. The data provide a weak constraint on the cover- ing fraction f of coronal bright spots. The disk- averaged brightness temperature Tb, reported in Table 4, is a combination of the stellar disk bright- ness temperature Tdisk and the coronal brightness temperature Tcor:
Tb = (1 − f) Tdisk + f Tcor (2) The minimum observable stellar disk brightness temperature at any wavelength is the tempera- ture minimum, but for simplicity we assume that the minimum stellar disk brightness temperature is Teff (listed in Table 1), the photospheric temper- ature. Assuming a typical coronal temperature of 106 K, we obtain covering fractions of 0.007, 0.003, and 0.005 for τ Cet, η Cas A, and 40 Eri A, respec- tively. The true covering fractions are likely lower because the stellar disk should have chromospheric brightness temperatures higher than Teff , and be- cause these stars have similar levels of magnetic ac- tivity to the Sun, in which the corona contributes insignificantly to the disk-integrated 35-GHz radi- ation. 3. Argue that coronal bright spots contribute insignif- icantly to solar 35-GHz emission: (a) Spatial argument: is the Sun pretty much a homogeneous disk at 35 GHz (can I find some 35-GHz images of the Sun throughout the so- lar cycle?) (b) Time argument: Nobeyama observations of the disk-integrated solar brightness temper- Fig. 2.— Brightness temperature spectra for the observed stars. ature spectrum at solar minimum and maxi- Non-detections are shown as 3-sigma upper limits (downwards ar- mum, reported in White (2004), show no vari- rows) and detections as points with one-sigma error bars. The plots ation in 35-GHz emission during the solar cy- also show the solar brightness temperature spectra from White cle, indicating that very little of the integrated (2004) for solar minimum (solid line) and solar maximum (dotted line). The solar cycle mainly affects the solar spectrum below 15 emission comes from bright spots above active GHz, where gyroresonant emission from active regions contributes regions, since active region coverage varies significantly to the emission, because the number and strength of with the solar cycle. active regions varies with the solar cycle. Above 15 GHz, solar ra- diation is predominantly chromospheric thermal free-free emission, (c) In contrast, the solar brightness tempera- which is constant throughout the solar cycle because the tempera- ture spectra reported in Loukitcheva et al. ture of the chromosphere remains steady. (2004) and Fontenla et al. (2007) show vari- ation in 35-GHz emission (by how much?) during the solar cycle. The brightness tem- peratures reported in these papers are disk- center brightness temperatures, rather than disk-integrated, which may lead to more vari- ation. In addition, the scatter of the reported 6
brightness temperatures is high because they 4. The level of free-free emission can be directly cal- include brightness temperatures from as early culated from LX if the entire corona is optically as 1950-ish (exact date?), when less accu- thin at a given frequency. rate absolute flux calibrations were available. (Maybe just write to Stephen White and ask 5. If parts of the corona are optically thick to him about this? Also it would be fantastic to bremsstrahlung at that frequency, then the radio get numbers and error bars from him instead luminosity will be lower than that predicted from of squinting at a plot.) the optically-thin calculation, so the assumption that the radio emission from the corona is opti- 4.2.1. Gyroresonance emission cally thin will yield an upper limit on the coronal 1. eqn for frequency at low gyroresonant harmonics radio luminosity.
2. For gyroresonant radiation in the s=3 harmonic, 6. To calculate emission measure from LX requires 34.5-GHz radiation requires the existence of mag- the X-ray emissivity ΛX (T ) - assumes isothermal netic field strengths of 4.1 kG. source: LX ≈ ΛX (T ) × EM (3) 3. Zeeman broadening: −23 3 (a) Zeeman broadening measures f*B, whereas 7. ΛX (1 MK) is approximately 10 erg cm /s for a gyroresonance measures B and constrains f ∗ passband of 8 to 80 A,˚ which is the closest match in Mewe et al. (1985) to the 0.1 to 2 keV (6 to 125 Tcor ˚ (b) Upper limits on Zeeman broadening for these A) ROSAT HRI passband. Failing to include 80 stars? I have some info on this but we should to 125 A˚ in the emissivity increases the estimated talk it through and I should read the papers emission measure and thus the expected level of a bit more before I bother writing it up. radio emission, so this calculation may overpredict the expected levels of radio emission by a factor of (c) (maybe in conclusions instead) A program of a few. (Is there a reference for X-ray emissivity in- simultaneous observations of Zeeman broad- tegrated over the RASS or ROSAT HRI passband? ening and microwave intensity should show This has got to exist but I didn’t know where to correlated time variation of the Zeeman look for it. I could do the integral myself from the broadening signal and the microwave flux if extensive tables of line and continuum emissivities gyroresonance is contributing appreciably to in Mewe et al. (1985) but that seems like a lot of the microwave flux. work.) 4. Discuss circular polarization 8. We used the X-ray-derived emission measure to cal- (a) Expected circular polarization of gyroreso- culate free-free luminosity LR: nance - from a single polarity region it’s very high, but when averaged over the stellar disk 9. Equation for 34.5-GHz flux based on LX , where with regions of various strengths and polari- jν,ff is the 34.5-GHz free-free emission coefficient 6 ties there might be a moderate circular polar- for 10 -K gas, calculated from Equation 20 in Dulk ization (1985): (b) The detection of circular polarization would L 4πj S = X ν,ff (4) be a smoking gun for gyroresonant emission, ν 4πd2 Λ but the lack of circular polarization does not X T −1/2 d −2 imply that it is not contributing to the emis- S = (560 µJy) ... sion ν 106 K 1 pc (c) Our constraints on circular polarization L Λ −1 X X (5) 4.2.2. Free-free emission 1027 erg/s 10−23 cm3 erg/s
1. Thermal emission from coronal plasma, at Mega- 10. The stellar X-ray luminosities in Table 2 yield ex- Kelvin temperatures, dominates the stellar X-ray pected 34.5-GHz fluxes due to coronal free-free luminosity. emission of 12.4, 42.7, and 32.7 µJy for τ Cet, η 2. As reviewed by G¨udel(2004), a majority of stud- Cas A, and 40 Eri A, respectively. These predicted ies have found that there are no significant optical fluxes do not contradict the lower detected fluxes depth effects in all stellar coronae except perhaps for η Cas A and 40 Eri A, because, as noted above, those of the most active stars, so we can safely as- the true levels of free-free emission are likely lower sume that the X-ray emission is optically thin. due to an underestimation of the X-ray emissivity and the assumption in this calculation that the en- 3. Since the coronal X-ray emission is optically thin, tire corona is optically thin at the observed radio the X-ray luminosity can be used to estimate the frequencies. We cannot rule out the contribution 2 coronal emission measure (the integral of ne over of coronal free-free emission to the detected stellar the coronal volume) and therefore constrain the radio emission on the basis of the stellar X-ray lu- free-free emission from the stellar corona. minosities (unless we get a more accurate, higher 7
value for X-ray emissivity over the ROSAT HRI ionized mass loss rate (since only ionized gas passband). contributes to the free-free emission). The 34.5-GHz optical depth is extremely low for 11. I got this idea from some lecture notes by Manuel any solar-like wind. Gudel from a plasma summer school - in them he includes an “X-ray covering fraction”, as well as a (d) Since the wind is optically thin, the radio lu- factor of 2 (since you’re not seeing both sides...?) minosity is obtained by integrating the free- which I did not understand so I did not include it free emissivity over the wind volume (from here the stellar surface to infinity), yielding an ex- pected 34.5-GHz flux of: 4.3. Diffuse coronal and stellar wind emission −1/2 −1 −5 T R∗ 1. Perhaps mention how even the optically-thin Sν = 2.9 × 10 µJy 6 ... corona may contribute appreciably to the bright- 10 K R !2 ness temperature because of the temperature in- M˙ v −2 d −2 version - a 106-K component with optical depth ion w −14 of 0.1 over an optically-thick 104-K chromosphere 10 M /yr 500 km/s 1 pc 5 would have Tb of 10 K. (7) 2. The diffuse corona that lies on open field lines This equation works for frequencies near 34.5 (i.e., not above action regions) flows into the stel- GHz and electron temperatures near 106 K. lar wind. This gas may also contribute to the net More general formulas must include slight ad- free-free radio emission observed from the star. justments to the exponents on frequency and temperature to account for the dependence of 3. The Lx to Lr calculation in the previous section the Gaunt factor on these quantities (see for constrains the free-free radio emission from the en- example Equation 24b in the review of stellar tire corona, not just the part above active regions, radio emission by G¨udel(2002)). so it is clear that coronal free-free emission does not dominate the observed stellar microwave emission. (e) Equation 4d makes it apparent that a stel- lar wind will not contribute detectably to the 4. We can also estimate expected levels of free-free ra- stellar radio emission at 34.5 GHz, unless any dio emission from the magnetically-open corona by of these stars had a mass loss rate more than assuming a stellar wind with solar-like properties. 1000 times the solar mass loss rate. (If Manuel Gudel’s student is publishing her paper soon (a) The Sun loses mass through the solar wind at about winds of young solar analogs it could −14 a rate of 2-3×10 M /yr. The solar wind be mentioned here.) has a fast component and a slow component, within which different elements have a differ- (f) This stands in contrast to radiation pressure- ent velocities, as reviewed in reviewed in As- driven winds from massive stars, which can chwanden et al. (2001). The base of the so- produce radio emission of 100s of µJy or more lar wind has coronal temperatures, typically at kiloparsec distances (Scuderi et al. (1998)). around 1 MK. For the following stellar wind calculations, we scale the equations for an “av- 4.4. Non-thermal gyrosynchrotron emission erage” solar wind speed of 500 km/s and a Evidence for the gyrosynchrotron emission mechanism wind temperature of 1 MK, and an ionized in active stars lies in suprathermal disk-averaged bright- −13 mass loss rate of 10 M /yr. ness temperatures (e.g., reference?), which are not ob- (b) We assume a spherically-symmetric, constant- served in these stars. Additionally, at GHz frequencies velocity wind with a steady mass loss rate, the Sun does not flare at a sufficient rate to produce implying a 1/r2 density profile. These sim- the “quiescent” non-thermal gyrosynchrotron radiation plifying assumptions, combined with the as- observed in magnetically active stars. Since the ob- sumed solar wind properties, should provide served stars have solar-like levels of magnetic activity and an estimate of the stellar wind radio flux at brightness temperatures consistent with thermal emis- an order-of-magnitude level. sion, gyrosynchrotron radiation is unlikely to contribute appreciably to the detected 35-GHz radio emission. (c) Using Equation 20 of Dulk (1985) to calculate These stars are not expected to obey the X-ray-radio the optical depth of a stellar wind with solar- luminosity relationship observed in active stars, since like properties, we obtain: that relationship is based on stars with non-thermal at- −2 −3/2 mospheres sustained by frequent flaring. The relation- −10 ν T τ = 2.0 × 10 ... ship in ?, log10 LR = log10 LX − 15.5, predicts 5- to 8.5- 34.5 GHz 106 K GHz fluxes of 10, 26, and 150 µJy for τ Cet, η Cas A, !2 and 40 Eri A respectively, based on the X-ray luminosi- r −3 M˙ v −2 ion w ties from Table 2. The LX -LR relationship shows roughly −14 (6) R 10 M /yr 500 km/s an order of magnitude of scatter, so the upper limit on 15-GHz emission from 40 Eri A is at the low end of the where r is the distance of the line of sight expected range if the star did follow the X-ray-radio lu- from the center of the star and M˙ ion is the minosity relationship. 8
4.5. Flare emission 4. SKA: track polarization reversals over course of [Need to produce time series to write this section. I stellar cycle - need ∼0.1 uJy sensitivity to get rc to don’t think we have enough SNR to make a strong state- ±0.2 ment about variability but we can potentially rule out very large, short-duration flares, as well as a certain level 5.2. Temperature profiles of stellar atmospheres of variation between different dates. We can use the time series to check whether the observed emission at different 1. Combine ALMA and VLA data to create Tb(ν) times is consistent with steady, quiescent emission.] profile, showing increasing temperatures at increas- ing atmospheric heights - constrain chromospheric 5. CONCLUSIONS models such as Fontenla et al. (2007) through ap- Recap: detection of 34.5-GHz radio emission from plication to other, nearby stars. solar-type stars (tau Cet, eta Cas A, 40 Eri A) 1. most likely thermal chromospheric emission 2. Constraints would be even stronger when combined with far-infrared data to observe the temperature 2. contribution from coronal thermal gyroresonance minimum, as in Liseau et al. (2013). above active regions not well constrained by data, 3. Other types of stars: VLA is now sensitive enough but unlikely to be large based on solar observations to detect thermal emission from non-magnetic A stars - check if they have a temperature inversion, 3. constraints on spectral index and circular polariza- especially in the case of X-ray-emitters without a tion known (low-mass) companion - this is based on Drake et al 1993, which brought this up as a bit of 4. maybe fit in here somewhere that thermal stellar mystery (why they would be X-ray emitters with- emission from low-mass main-sequence stars has out having measured magnetic fields) - don’t know not been detected until now because all previous what the status of this is today - maybe the B fields radio detections of such stars were only active stars, just weren’t strong enough to measure back in the in which the non-thermal gyrosynchrotron compo- day? anyways it could be interesting to see if they nent dominates the radio emission have a temperature inversion in the stellar atmo- 5. summarize constraints on other forms of emission? sphere (which would be consistent with the X-ray emission) - disk-averaged Tb indicative of temperature inversion above photosphere (already confirmed by X-ray data? 6. ACKNOWLEDGEMENTS but this is an independent method) - (weak) constraints on mass loss rate - potentially sen- VLA: The National Radio Astronomy Observatory is sitive to mass loss rates of young solar analogs? a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, 5.1. Tracking the magnetic activity cycles of solar-type Inc. stars NSF GRFP: This material is based upon work sup- ported by the National Science Foundation Graduate Re- 1. Radio flux offers a new diagnostic for tracking the search Fellowship under Grant No. (NSF grant number). magnetic activity cycle of nearby stars. [get grant number from CO - what’s a CO?] 2. The 35-GHz flux of the observed stars is unlikely Eric Mamajek of the University of Rochester for to vary over the stellar cycle, although detected his excellent web page discussing solar properties periodic variation would indicate a higher covering and references, “Basic Astronomical Data for the Sun” fraction of strong magnetic fields than on the Sun. (https://sites.google.com/site/mamajeksstarnotes/basic- astronomical-data-for-the-sun). 3. Potential for a deeper VLA survey to detect ∼4-12 US Naval Observatory’s 6th Catalog of Visual Binaries GHz emission - expect flux to change by roughly and the calculator a factor of 2 over the course of the stellar activity This research has made use of the SIMBAD database, cycle. operated at CDS, Strasbourg, France.
REFERENCES Aschwanden, M. J., Poland, A. I., & Rabin, D. M. 2001, di Folco, E., Absil, O., Augereau, J.-C., et al. 2007, A&A, 475, 243 ARA&A, 39, 175 Donahue, R. A., Saar, S. H., & Baliunas, S. L. 1996, ApJ, 466, 384 Baliunas, S., Sokoloff, D., & Soon, W. 1996, ApJ, 457, L99 Drake, S. A., Simon, T., & Brown, A. 1993, ApJ, 406, 247 Bastian, T. S., Benz, A. O., & Gary, D. E. 1998, ARA&A, 36, 131 Dulk, G. A. 1985, ARA&A, 23, 169 Benz, A. O., & G¨udel,M. 1994, A&A, 285, 621 Fontenla, J. M., Balasubramaniam, K. S., & Harder, J. 2007, Bouvier, A., & Wadhwa, M. 2010, Nature Geoscience, 3, 637 ApJ, 667, 1243 Boyajian, T. S., McAlister, H. A., van Belle, G., et al. 2012, ApJ, Gray, R. O., Corbally, C. J., Garrison, R. F., et al. 2006, AJ, 132, 746, 101 161 Canto Martins, B. L., Das Chagas, M. L., Alves, S., et al. 2011, Gray, R. O., Graham, P. W., & Hoyt, S. R. 2001a, AJ, 121, 2159 A&A, 530, A73 Gray, R. O., Napier, M. G., & Winkler, L. I. 2001b, AJ, 121, 2148 Condon, J. J., Cotton, W. D., Fomalont, E. B., et al. 2012, ApJ, Greaves, J. S., Wyatt, M. C., Holland, W. S., & Dent, W. R. F. 758, 23 2004, MNRAS, 351, L54 Demory, B.-O., S´egransan,D., Forveille, T., et al. 2009, A&A, G¨udel,M. 1992, A&A, 264, L31 505, 205 —. 2002, ARA&A, 40, 217 9
—. 2004, A&A Rev., 12, 71 Mewe, R., Gronenschild, E. H. B. M., & van den Oord, G. H. J. G¨udel,M., & Benz, A. O. 1993, ApJ, 405, L63 1985, A&AS, 62, 197 G¨udel,M., Schmitt, J. H. M. M., & Benz, A. O. 1994, Science, Orchiston, W. 2005, Journal of Astronomical History and 265, 933 Heritage, 8, 3 Heintz, W. D. 1974, AJ, 79, 819 Schmitt, J. H. M. M., & Liefke, C. 2004, A&A, 417, 651 Hey, J. S. 1946, Nature, 157, 47 Scuderi, S., Panagia, N., Stanghellini, C., Trigilio, C., & Umana, Holmberg, J., Nordstr¨om,B., & Andersen, J. 2007, A&A, 475, 519 G. 1998, A&A, 332, 251 Judge, P. G., Solomon, S. C., & Ayres, T. R. 2003, ApJ, 593, 534 Southworth, G. C. 1945, Microwave Radiation from the Sun (with Liseau, R., Montesinos, B., Olofsson, G., et al. 2013, A&A, 549, Erratum), ed. W. T. Sullivan, III, 168 L7 Teixeira, T. C., Kjeldsen, H., Bedding, T. R., et al. 2009, A&A, L´opez-Santiago, J., Montes, D., G´alvez-Ortiz, M. C., et al. 2010, 494, 237 A&A, 514, A97 van Leeuwen, F. 2007, A&A, 474, 653 Loukitcheva, M., Solanki, S. K., Carlsson, M., & Stein, R. F. White, S. M. 2004, New Astronomy Reviews, 48, 1319 2004, A&A, 419, 747 Wilsing, J., & Scheiner, J. 1896, Annalen der Physik, 295, 782 Mamajek, E. E., & Hillenbrand, L. A. 2008, ApJ, 687, 1264 Mason, B. D., Wycoff, G. L., Hartkopf, W. I., Douglass, G. G., & Worley, C. E. 2013, VizieR Online Data Catalog, 1, 2026