Is the Vega Debris Disk
Evolving in a Steady State?
Sebastian Müller, Torsten Löhne, and Alexander V. Krivov
Astrophysikalisches Institut und Universitäts-Sternwarte, Friedrich-Schiller-Universität, Schillergässchen 2–3, 07745 Jena, Germany
www.astro.uni-jena.de, sebastian@astro.uni-jena.de, tloehne@astro.uni-jena.de, krivov@astro.uni-jena.deseit 1558

Abstract

The Vega System

Debris disks, the left-overs of planet formation, consisting of dust and dustproducing planetesimals, are nowadays known to be common around mainsequence stars. The first detection was made around the A0V star Vega in
1984. Since then, that system has been subject of many follow-up investigations. However, it is still under debate which mechanisms drive the productionof the observed dust. There have been claims that the standard assumptionof a steady-state collisional cascade is not capable of reproducing the observations. To check this, we modeled the Vega disk with our collisional code andcalculated the resulting spectral energy distribution (SED) as well as the radial surface brightness profiles for the Spitzer/MIPS wavelengths 24, 70, and160 µm to compare them to all available observations. We find a reasonable fit
both to the observed SED over a broad spectral range from mid-IR to mm andto the brightness profiles. Our conclusion is that the Vega disk does not seemto be incompatible with the standard, steady-state evolutionary scenario.

The Vega disk was resolved with several instruments in the sub-mm region showing a pole-on, clumpy ring[e.g., 8]. As sub-mm emission is dominated by larger, colder grains, the ring probably points to a dust-producing
planetesimal belt. Spitzer/MIPS images at 24, 70 and 160 µm revealed a much more extended, featureless,symmetric disk [7]. The interpretation is that the distribution of smaller, hotter dust from the same belt, responsible
for the warmer emission, is broadened and smoothed by radiation pressure forces. The composite image on theright-hand side combines the far-IR disk image at 70 µm [7] with the sub-mm one at 350 µm [8].
Vega is known to be a fast rotator [5, 6]. Thus, the stellar properties seen by the disk differ from those that are seenby the observer. The table below lists key parameters of the star:equatorpole
R[5][R⊙]
2.873 ± 0.026 2.306 ± 0.031[6]
Teff [K]7 900+500
10 150 ± 100−40057 ± 3L∗[L⊙]
28+8−6log(g[cm/s2 ])[5] 4.074 ± 0.012 3.589 ± 0.056[6]M∗ [M⊙]
2.3 ± 0.2
Age[Myr]
350

ModelsSUBITO: SUrface Brightness Investigation TOol
A code that calculates the radial surface brightness profile and convolves
it with the stellar point spread function (PSF). The resulting profile is thencompared to the observed one. If resolved observations are available(which is the case for the Vega disk), a combined analysis of SED andbrightness profiles allows us to break some of the degeneracies known tobe typical of the SED fitting.
It is not to be expected that a first guess of model parameters will lead directly
to a perfect match with the observations, so that the whole simulation (ACESEDUCE-SUBITO) has to be repeated with different model parameters. To
get an impression of how the model has to be modified we compare the dust
distribution with the temperature profile to see which regions in the grain
size and spatial distribution need to be altered. Such a comparison for our“nominal” model 1 (see table on the right) is shown in the figure.

60AU
100AU
300AU

100

102

102

101

101

100

100

10-110-1s [µm]SEDUCE: SED Utility for Circumstellar Environment
Assuming the particles to be in thermal equilibrium with the stellar radiation, the code calculates the spectral energy distribution (SED), from thedust portion of the modeled disk. Using appropriate scaling laws [3], thecalculated SED can be scaled to the observed one.

Model 1 is our first-guess, “nominal” model. In the others, we vary: stellar luminosity; location, extension, excitation, and thickness of the disk; dust composition;
collisional outcome prescription. Models 2 and 13 assume a reduced luminosity
at the stellar equator, as expected for a rapidly rotating star. The nominal grainmodel is based on Mie calculations for astronomical silicate [9]. For models 8and 9, we applied Maxwell-Garnett theory to produce inhomogeneous grains with
10% iron or water ice inclusions embedded in an astrosil matrix. The nominal
collisional prescription includes disruptive and cratering collisions [3]. In model 10
the cratering efficiency was lowered; in model 11 only destructive collisions wereconsidered. The maximum in the size distribution in model 12 was broadened
artificially to emulate an expected scatter of optical and mechanical properties ofgrains in a realistic disk.

103200s [µm]ACE: Analysis of Collisional Evolution
A collisional code to generate a debris disk from an assumed ring of planetesimals and then to follow the evolution of the size and spatial distribution of all solids in the disk, from planetesimals to dust [1, 2].

10350

model L∗[L⊙] ainner [AU] aouter [AU] emax sin ǫ composition collisional outcome
1
37
70
100
0.2 0.1
astrosilnominal case
225
70
100
0.2 0.1
astrosilnominal case
337
50
100
0.2 0.1
astrosilnominal case
437
70
120
0.2 0.1
astrosilnominal case
537
50
120
0.2 0.1
astrosilnominal case
6
37
70
100
0.1 0.05
astrosilnominal case
7
37
70
100
0.4 0.2
astrosilnominal case
837
70
100
0.2 0.1 iron incl.
nominal case
937
70
100
0.2 0.1
ice incl.
nominal case1037701000.2 0.1
astrosilweak crat.
113770100
0.2 0.1
astrosilno crat.
1237
70
100
0.2 0.1
astrosilsmoothed size distr.
1325
70
100
0.2 0.1
astrosilsmoothed size distr.

10-23 10-22 10-21 10-20 10-19
A [cm2 cm-3]

10-19
A [cm2 cm-3]

To reproduce the observational data, we consecutively employ three numerical tools:

Tg [K]

Approach

10-20
10-21
10-22

2.9 µm
7.5 µm
10-23 19 µm
198 µm
10100r [AU]Results
Dust Composition

Stellar Luminosity
and Disk Location

Collisional OutcomeBest ModelStarObservations

102

102

101

101

1892
34
1000

10100

λ [µm]

Sν [mJy/arcsec2]

100

1000

10100

λ [µm]

1000

λ [µm]

24 µm

100

10-1-210Sν [mJy/arcsec2]

10

λ [µm]

100

Sν [mJy/arcsec2]

1000

10-1

1892
34

10
11
1110-2
13

70 µm
100

100

10-1

10-1
160 µm

100

100

10-1

10-1

100

150

200

250
r [AU]

300

350

400

100

150

200

250
r [AU]

300

350

400

100

Sν [mJy/arcsec2]

100

13150

200

250
r [AU]

300

350

400

100

150

200

250r [AU]

300

350

Sν [mJy/arcsec2]

10101112Fν [mJy]103

Fν [mJy]

103

104

Sν [mJy/arcsec2]

104

400

Conclusions

References

Acknowledgements

We have modeled a steady-state collisional evolution of the Vega debris disk, calculated its thermal emission, and compared the results withavailable resolved observations and photometry. Our first-guess model revealed two discrepancies: (1) a lack of 24 µm emission, and (2) atoo steep drop in the SED in the far-IR. Accordingly, we varied the stellar luminosity, the chemical composition of dust, the disk’s location andextension (within reasonable limits), its dynamical excitation, and the model of collisional outcomes. We find that neither the chemical composition
nor the disk parameters can alter the emission properties significantly. In contrast, the adopted stellar luminosity and the collisional outcomeprescription both have noticeable impact on the results. For instance, inclusion of cratering collisions seems mandatory to correctly reproduce theobserved sub-mm emission.

[1] Krivov et al.: A&A, 455 (2006), 509–519

Assuming a reduced stellar luminosity, as expected at the equator of the rapidly rotating star, fixes the problem (1) with the lacking 24 µmemission. To overcome the problem (2), a steep drop in the far-IR, we need a broader size distribution around its maximum. We speculate thata broader size distribution could result, for instance, from a scatter in optical and mechanical properties of dust particles in a realistic disk. We
mimick the effect by artificially broadening the size distribution to show that the problem (2) can indeed be eliminated.

[7] Su et al.: ApJ, 628 (2005), 487–500

We thank Kate Su and Mark Wyatt for providing the observed surface brightness
profiles and the corresponding pointspread functions. Fruitful discussions with
Hiroshi Kimura, Kate Su, Mark Wyatt,
Olivier Absil, Jean-Charles Augereau andHervé Beust are appreciated.
This work was partly funded by theDeutsche
Forschungsgemeinschaft(DFG). One of us (SM) is funded by
the Graduate Student Fellowship of theThuringia State.

We conclude that the debris disk of Vega seems to be compatible with a standard, steady-state evolution scenario.

[2] Löhne et al.: ApJ, 673 (2008), 1123–1137[3] Krivov et al.: ApJ, 687 (2008), 608-622[4] Müller et al: in prep
[5] Peterson et al.: Nature, 440 (2006), 896–899[6] Aufdenberg et al.: ApJ, 645 (2006), 664- 675[8] Marsh et al.: ApJL, 646 (2006), L77–L80[9] Laor, Draine: ApJ, 402 (1993), 441–468