Dual-band, Multi-aperture Polarization Measurements of β Pictoris

β Pictoris (HD 39060), is a nearby young A5 V star hosting a substantial debris disk that has been studied extensively from optical to millimeter wavelengths (e.g., Smith & Terrile 1984; Mouillet et al. 1997; Vandenbussche et al. 2010; Dent et al. 2014) and two planetary companions (Lagrange et al. 2010; Nowak et al. 2020). Its debris disk was the first to be directly imaged in scattered light (Smith & Terrile 1984), becoming a key system for the understanding of debris disks, exoplanets, and their mutual interactions (e.g., Dawson et al. 2011).

Spatially resolved scattered light measurements revealed an edge-on asymmetric disk extending several hundred astronomical unit from the star (Gledhill et al. 1991; Kalas & Jewitt 1995; Voshchinnikov & Krügel 1999). The dust polarization fraction increases with distance, peaking ∼20% at 300 au separation, with weaker NIR polarization compared to optical (Krivova et al. 2000; Tamura et al. 2006).

Here we present multi-aperture, dual-band measurements of the β Pictoris system using HIgh Precision Polarimetric Instrument 2 (HIPPI-2; Bailey et al. 2020). This polarimeter and its predecessor have been used extensively to study nearby stars with circumstellar dust (Marshall et al. 2016, 2020, 2023; Cotton et al. 2017).

Polarimetric observations of β Pictoris were made during the 2018 February (commissioning) and March HIPPI-2 observing runs at the 3.9 m Anglo-Australian Telescope (AAT). HIPPI-2 was mounted at the f/15 focus in February (Run 1), and f/8 in March (Run 2)—where a 2× Barlow lens was used for an effective f/16. Measurements were made in SDSS $g^{\prime}$ and $r^{\prime}$ with, respectively, blue and red sensitive PMTs, giving λ_eff ≈ 465 and 623 nm for each combination. Aperture diameters spanned 5''–25'', equivalent to radii of 50–250 au at 20 pc (van Leeuwen 2007).

Full calibration details are described in Bailey et al. (2020), except here we adopt an updated modulator efficiency determination: λ₀ = 516.6 nm, Cd = 1.995 × 10⁷ nm³, ${e}_{\max }=98.5 \%$. Centering, accurate to ∼05, was performed manually (by JB) with fixed offset R.A./decl. buttons using real-time PMT feedback. AAT seeing is typically 1''–2'', blurring the disk radii probed.

Table 1 gives the observed total linear polarization, $p=\sqrt{{(Q/I)}^{2}+{(U/I)}^{2}}$, and position angle, $\theta =\tfrac{1}{2}{\tan }^{-1}(U/Q)$, where I, Q and U are Stokes parameters. Also presented is the data with interstellar polarization subtracted; it being described by a Serkowski–Wilking Law with ${\lambda }_{\max }=470\,\mathrm{nm}$, ${p}_{\max }=30.7\pm 0.9\,\mathrm{ppm}$, and θ_i  = 466 ± 0.6 (Marshall et al. 2023).

Table 1. Aperture Polarization Measurements of β Pictoris

			Green ($g^{\prime}$) Measurements					Red ($r^{\prime}$) Measurements
		Model		Raw		IS Subtracted			Raw		IS Subtracted
DAp	Rd	Fd/F⋆	Run	p	θ	p	θ	Run	p	θ	p	θ
('')	(au)	(%)		(ppm)	(°)	(ppm)	(°)		(ppm)	(°)	(ppm)	(°)
5.3	52.0	5.523						2 a	107.2 ± 8.0	119.4 ± 2.1	132.1 ± 8.1	123.0 ± 1.7
5.7	56.0	5.657	1	112.2 ± 5.5	113.4 ± 1.4	135.1 ± 5.6	118.1 ± 1.2
8.6	84.4	6.125						2	145.8 ± 7.9	115.8 ± 1.6	168.5 ± 8.0	119.1 ± 1.4
9.2	90.3	6.170	1	147.4 ± 5.1	112.5 ± 1.0	169.4 ± 5.2	116.4 ± 0.9
11.9	116.8	6.294						2	186.1 ± 7.5	117.8 ± 1.2	209.7 ± 7.6	120.2 ± 1.1
12.7	124.7	6.316	1	190.1 ± 5.2	113.2 ± 0.8	212.2 ± 5.3	116.2 ± 0.7
15.7	154.1	6.369	2	180.0 ± 4.5	114.6 ± 0.7	203.1 ± 4.6	117.6 ± 0.6	2	196.6 ± 7.7	116.0 ± 1.1	219.1 ± 7.7	118.5 ± 1.0
16.8	164.9	6.382	1	193.0 ± 5.1	114.5 ± 0.8	215.9 ± 5.2	117.3 ± 0.6
18.7	183.6	6.398	2	207.9 ± 4.8	116.3 ± 0.7	231.9 ± 4.9	118.7 ± 0.6	2	214.6 ± 7.5	119.2 ± 1.0	238.8 ± 7.6	121.2 ± 0.9
25.5	250.3	6.429	2	186.5 ± 4.9	120.1 ± 0.7	212.8 ± 5.0	122.4 ± 0.7

Note.

^a Previously reported in Marshall et al. (2023).

3.1. Trends with Wavelength and Disk Radius

3.2. Calculations of Scattered Light Polarization

For an idea of how polarizing the grains are for comparison with other estimates, we make some simplistic calculations. We assume the ratio of disk to stellar surface brightness as a function of radius in $g^{\prime}$ and $r^{\prime}$ is the same as in I band, as described by Smith & Terrile (1984), where particle number density decreases ∝r^−3.1. We then approximate the disk structure as a single-scattering annulus of height 89 au, extending 30–500 au, and calculate the disk flux (F_d) in each aperture by adding concentric 1 au rings. Where the aperture cuts the disk, the fractional ring contribution is,

$$\begin{eqnarray}&&f=r[2\pi -4\arccos ({R}_{\mathrm{Ap}}/r)],\end{eqnarray} \tag{ 1 }$$

where r and R_Ap are the ring and aperture radii respectively.

We can minimize the impact of geometric cancellation by subtracting the interior of two outer apertures (where our model is also more accurate Artymowicz et al. 1990). Taking—as indicative of the general trend—the difference in scattered light contribution between 157 and 187 diameter apertures (R_d  = 154.1–186.3 au) we scale the corresponding polarization differences to give 10% ± 2% in $g^{\prime}$ and 6% ± 4% in $r^{\prime}$. Since there will still be some cancellation, these values represent a lower limit. Given the crudeness of the model/approximations, this agrees very well with the data collated by Krivova et al. (2000), which shows polarization of 12%–15% and rising at 200 au, where the lower values are for R compared to B band. Krivova et al. (2000)'s models predict lower polarizations for interior radii, our results are consistent with that general trend, with values as low as ∼0.1% for radii between ∼50 and 90 au, though those determinations are increasingly suppressed by geometric cancellation.

We observed the iconic debris disk host star β Pictoris in $g^{\prime}$ and $r^{\prime}$ bands using the aperture polarimeter HIPPI-2 on the 3.9 m AAT. We detected substantial polarization from the system originating from its edge-on debris disk. The magnitude of polarization increases with aperture diameter out to 19'', consistent with previous measurements. Our observations probe angles comparable to available high-contrast optical/NIR imaging; no evidence is found to refute models predicting smaller polarizations at interior radii. We find no polarization color dependence, consistent with polarization arising through scattering from large dust grains.

This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of NASA's Astrophysics Data System. J.P.M. acknowledges research support by the National Science and Technology Council of Taiwan under grant NSTC 112-2112-M-001-032-MY3. D.V.C. thanks the Friends of MIRA for their support. Based on data obtained at Siding Spring Observatory. We acknowledge the traditional owners of the land on which the AAT stands, the Gamilaraay people, and pay our respects to elders past and present.

Facility: Anglo Australian Telescope - .

Software: Python, Numpy, Scipy, Microsoft Excel.