BRIGHT DEBRIS DISK CANDIDATES DETECTED WITH THE AKARI/FAR-INFRARED SURVEYOR

Our solar system is a debris system with the asteroid belt at 2–3.5 AU and the Kuiper Belt at 30–48 AU (Kim et al. 2005). Debris disks have been detected in the extrasolar stellar systems as well, commonly referred to as "The Vega Phenomenon" (Silverstone 2000). The stars with debris disks are generally much older than 10 Myr (Krivov 2010), which is much longer than the typical timescale of collisional destruction of dust grains or of spiraling inward due to Poynting–Robertson drag. Thus, dust grains have to be continuously replenished by collisions and/or evaporation of planetesimals (Backman & Paresce 1993; Wyatt 2008). The studies of debris systems are significant because they provide a better understanding of the formation and evolution of planetesimal belts and planetary systems (Zuckerman & Song 2004; Moór et al. 2011; Raymond et al. 2011, 2012).

The first extrasolar debris disk was detected by the Infrared Astronomical Satellite (IRAS) around Vega in 1983 (Aumann et al. 1984). Until recently, nearly a thousand debris disks had been detected. Most of these systems were found through the detection of infrared (IR) excess over the stellar photospheric emission. The IR excess is explained as the dust re-radiation of the absorbed starlight. At the sensitivity level of the Multi-band Imaging Photometer on Spitzer (Werner et al. 2004; Rieke et al. 2004), the incidence of debris disks around main-sequence (MS) stars is about 15% (Krivov 2010). Due to their small sizes, only dozens of debris disks around nearby stars have follow-up direct imaging observations in optical, mid-infrared (MIR), and submillimeter bands (e.g., Schneider et al. 2001; Greaves et al. 2005; Wyatt et al. 2005; Kalas et al. 2006; Su et al. 2008; Lagrange et al. 2012)¹.

The observed debris disks display diverse properties. Most debris disks have relatively low dust temperatures between 30 and 120 K, corresponding to disk sizes from several tens to 100 AU for type A to K stars (Chen et al. 2006; Moór et al. 2011; Plavchan et al. 2009; Rhee et al. 2007). A small subset of warm debris disks have been discovered recently with AKARI, Spitzer, and Wide-field Infrared Survey Explorer (WISE; Fujiwara et al. 2009, 2010a, 2010b, 2013; Meyer et al. 2008; Olofsson et al. 2012; Ribas et al. 2012), and the incidence of such disks drops very rapidly with the age of the stars (Urban et al 2012). More recently, Herschel revealed a population of cold debris disks extending to more than 100 AU with its good sensitivity to the long IR wavelength (Eiroa et al. 2011). A single temperature blackbody model usually provides a good fit to the MIR spectrum, suggesting that grains are distributed over a relatively narrow annulus (Schutz et al. 2005; Chen et al. 2006). The relatively narrow width has been confirmed for some debris disks by direct imaging in the IR and submillimeter bands (Booth et al. 2013).

The incidence of debris disks as a function of other stellar parameters is of great interest as it gives a further clue to its origin. It appears that the frequency of stars with debris disks is larger among earlier types of stars and decreases with the increase of stellar age (Rhee et al. 2007; Wyatt 2008). The rate appears to correlate with the presence of planets, but not the metallicity of the host stars (Maldonado et al. 2012). The general trend with stellar age reflects the consumption of planetesimals during the system evolution. However, interpretation of the correlation with stellar types may be more complex since early-type stars have much shorter lifetimes than late-type stars, and the correlation may be entirely caused by the age dependence of incidence. In addition, the detected debris disks displayed a wide range of IR excesses from 10⁻⁶ up to 10⁻² of stellar bolometric luminosity. Over such a wide range, different mechanisms of debris disks may operate; therefore, it would be interesting to examine the incidence at a certain fraction of IR excesses. To explore a large parameter space, a large unbiased sample of debris disks with known host parameters is required.

Until recently, debris disks have been discovered mostly based on the IR data from four satellites: IRAS (Mannings & Barlow 1998; Rhee et al. 2007), Infrared Space Observatory (ISO; Kessler et al. 1996; Oudmaijer et al. 1992; Abraham et al. 1999; Habing et al. 1999; Fajardo et al. 1999; Spangler et al. 2001; Decin et al. 2003), Spitzer (Beichman et al. 2006; Bryden et al. 2006; Chen et al. 2005; Kim et al. 2005; Moór et al. 2006, 2011; Rebull et al. 2008; Rieke et al. 2005; Siegler et al. 2007; Su et al 2006; Wu et al. 2012), and Herschel (Matthews et al. 2010; Eiroa et al. 2013). IRAS contained a cryogenically cooled telescope orbiting above the Earth's atmosphere to make an unbiased all-sky survey at 12, 25, 60, and 100 μm (Neugebauer et al. 1984) at a relatively poor spatial resolution (4'–5') and sensitivity (0.6 Jy at 60 μm in the Point Source Catalog and 0.225 Jy at 60 μm in the Faint Source Catalog).²Spitzer, ISO, and Herschel possess much better spatial resolutions and sensitivities than IRAS, but they cover much smaller areas of sky at mid- and far-infrared (FIR) bands. Thus, the latter missions discovered more faint debris disks. The latter satellites also carried pointed observations of nearby bright stars that were sensitive to the IR excess down to 10⁻⁶ of the host star luminosity.

In this paper, we search systematically for debris systems around MS stars by cross-correlating the Hipparcos catalog (Perryman et al. 1997) with the AKARI/Far-Infrared Surveyor (Kawada et al. 2007) All-Sky Survey Bright Source Catalogue (AKARIBSC; Yamamura 2010). AKARI/FIS surveyed all sky at FIR with a spatial resolution (48'') better than IRAS and at a sensitivity (0.55 Jy in 90 μm) comparable to IRAS. The higher resolution will significantly reduce the false contamination in comparison with IRAS. As in the IRAS studies, our work also focuses on the IR bright debris disks that complement the deep surveys from ISO and Spitzer. Our primary motivation is to search for FIR excess stars by AKARI/FIS and discuss the fundamental parameters of the disks such as dust temperature, fractional luminosity, and dust location. These parameters can be estimated from the spectral energy distribution (SED) of dust emission. Fortunately, all IR excess stars except HIP 57757 in our sample have WISE detections which lead to better wavelength coverage than many previous searches. As shown by Moór et al. (2011), the interpretation of a SED is ambiguous, but by handling a debris disk sample as an ensemble, one can obtain a meaningful picture about the basic characteristics of the parent planetesimal belt(s) and evolutionary trends. The paper is arranged as follows. We will describe the data sets and methods used in the construction of the debris disk sample in Section 2, present an analysis of the properties of the disks as well as their host stars in Section 3, discuss the sample comparison in Section 4, and, finally, present the conclusion in Section 5.

2.1. Matches between Hipparcos catalog and AKARIBSC

The primary star catalog used in this work is the Hipparcos catalog, which contains over 110,000 stars with precise photometry, as well as astrometry of unprecedented accuracy for the nearby stars (Bessell 2000). In Figure 1, we show a Hertzsprung–Russell (H–R) diagram for all the cataloged stars by extracting the colors (B − V) and parallaxes from the Hipparcos database. The MS stars are selected according to the criterion M_V ⩾ 6.0(B − V) − 2.0 (Rhee et al. 2007). This results in a catalog of 67,186 Hipparcos MS stars.

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We then cross-correlate the catalog with the AKARIBSC to identify the Hipparcos MS stars detected in the AKARI/FIS bands. Since the AKARIBSC has much worse position precision than the Hipparcos catalog, we determine the matching radius based on the performance of AKARI only. The spatial distribution of the AKARI/FIS sources is very inhomogeneous on the sky, so a uniform matching radius is not an ideal choice. To show this, we write the false detection rate for a subsample of stars on the sky with the background surface density n of the IR sources as

$$\begin{equation} R_{{\rm false}}=\frac{N_{{\rm false}}}{N_{{\rm total}}}=\frac{N_* \pi r^2 n}{N_*fc(r)+N_*\pi r^2 n}= \frac{\pi r^2 n}{fc(r)+\pi r^2 n}\protect, \protect \end{equation} \tag{ 1 }$$

where f is the fraction of Hipparcos stars with IR fluxes above the detection limit. N_total and N_false are the number of all matches and the expected number of chance matches, respectively. c(r) is the completeness with a matching radius r, i.e., the probability of a real matching source falling within a circle of radius r around the star, which is determined by the position error ellipse of the IR source. Assuming n does not correlate with f, the fraction of false matching increases with the background surface density of IR sources at a given matching radius. In reality, f and n might be correlated, e.g., young stars are more likely located on the Galactic plane where the stellar surface density is also higher; as such, the false matching fraction may not follow Equation (1) exactly. Anyway, we will determine the matching radius according to the surface density of IR sources. Since c(r) increases slower than r², as r increases, the false matching rate increases.

As a trade-off between the reliability and completeness, the matching radius at a given surface density is so chosen that the false detection rate is less than 10%. In practice, we estimate the local AKARI/FIS source density around each Hipparcos star and then divide the Hipparcos stars into different density bins. For each bin, we can calculate the expected chance matches N_false at a given radius with N_*πr²n and get the total matched number N_total from the cross-correlation. Thus, the false detection rate R_false is given by N_false/N_total. We increase the matching radius in each bin iteratively from 5''to a radius where the false detection rate is close to 10% or to the upper limit of 20''. The cross-correlation results in 136 matching pairs. Figure 2 presents the number of the Hipparcos stars (upper panel), matched IR sources (middle panel), and matching radii (bottom panel) at each bin of the local IR source density. An interesting feature in this plot is that the peak of matched pair distribution is shifted to the high-density area rather than to the lower-density area as expected. This implies a strong correlation between f and n. Regions of lower density have a lower fraction of stars with bright debris disks perhaps because the chance of finding young stars in such regions is lower. While at higher-density regions, the higher excess fraction in the Galactic plane may be justifiable and the magnitude of this effect can be estimated from Figure 2, which looks like the fraction is fairly constant above ∼1 deg⁻², but a factor of six lower for lower far-IR densities.

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Next, we remove the sources with obvious contaminations in the IR. Seven stars in nebulae are rejected because a nebula is a FIR source. Among them, three stars are in Kalas's sample (Kalas et al. 2002), a nebula is clearly seen in the images of the other three stars returned by SIMBAD, and one additional star (HIP 78594) was rejected by Moór et al. (2006) based on the image of the Digitized Sky Survey, which shows a reflection nebulosity around this star. Another contamination source is the emission from cold diffuse interstellar dust (cirrus; Rhee et al. 2007), which also emits in the MIR (e.g., Boulanger & Pérault 1988). We reject the cirrus contamination stars based on their MIR images obtained by WISE (Wright et al. 2010). WISE has mapped the whole sky in IR bands W1, W2, W3, and W4 centered at 3.4, 4.6, 12, and 22 μm with 5σ point-source sensitivities better than 0.08, 0.11, 1, and 6 mJy, respectively. The angular resolutions are 61, 64, 65, and 120 at corresponding bands, and the astrometry precision for high SNR sources is better than 015 (Wright et al. 2010). The high-sensitivity and high-angular-resolution images are used to remove the confusion source and to further constrain the disk properties in the SED fitting. All stars except HIP 57757 are covered by WISE. We check the WISE images of these sources for the presence of weak diffuse emissions around stars. Seven stars are affected by potential cirrus emissions and rejected, leaving 122 stars for further study. Note that the number of rejected contaminated sources is in agreement with the expected chance matches.

2.2. Infrared Emission of Stellar Photosphere

Obtaining the flux densities of stellar photosphere is essential for identifying and measuring the strength of an IR excess (Bryden et al. 2006). We collect the optical to near-infrared (NIR) absolute photometric data of stars in our sample to construct SED. Optical magnitudes in B and V are taken from the Hipparcos satellite measurements. NIR photometries JHK_s are extracted from Two Micron All Sky Survey (2MASS) catalogs (Skrutskie et al. 2006). The observed magnitudes are converted into flux density (Janskys) using the zero magnitudes in Cox & Pilachowski (2000) (Rhee et al. 2007).

The stellar SEDs are fitted with the latest Kurucz' models (ATLAS9)³ (Castelli & Kurucz 2004). The models cover wide ranges of four parameters: temperature, surface gravity, metallicity, and projected rotational velocity. For each stellar type, we select only a subset of model spectra from ATLAS9 according to Allen's astrophysical quantities (Cox et al. 2000). For B-type stars, the effective temperatures are in 500 K increments from 10,000 to 20,000 K, and the surface gravity log g cm s⁻² value is 4.0. For A-type and later-type stars, the effective temperatures are in 250 K increments from 3500 to 10,000 K, and the surface gravity log g cm s⁻² values are 4.0, 4.5. We chose microturbulent velocity ξ = 2 km s⁻¹ and metallicity value [M/H] = 0 (solar metallicity) for all cases.

We fit the model spectra to the observed SED from optical to NIR for each object in order to find the best matched stellar model. During the fit, the stellar spectra are reddened and convolved with the response of each filter to yield the model flux density at each band. This method gives the model flux density more accurately than adopting a constant magnitude to flux conversion factor, especially when the passband includes significant spectral features such as the Balmer jump (Rhee et al. 2007). For each stellar model, the best fit is obtained by minimizing χ² with the extinction E(B − V) and normalization as free parameters. We select the best model with the smallest χ² among different stellar models. Using the best-fit Kurucz model, we estimate the stellar photospheric flux densities in the WISE and AKARI bands.

To assess the reliability of stellar photospheric flux predicted by the best model in the WISE W3 and W4 bands, we examine the distribution of the differences between observed and predicted magnitudes for a sample of randomly selected Hipparcos MS stars, which usually should not show MIR excesses. The sample is compiled so that the comparison sample well matches our final debris disk sample in the distribution of Galactic latitudes and stellar spectral types, as well as their optical magnitudes. The size of the comparison sample is a factor of two larger. We fit the optical to the NIR photometric data of the comparison sample with stellar models as described above. The distributions of the differences are fairly narrow with almost no systematical offsets (Figure 3): 〈W3(observed) − W3(model)〉 ≃ 0.002 mag, 〈W4(observed) − W4(model)〉 ≃ 0.04 mag, and σ(W3) = 0.06 mag and σ(W4) = 0.13 mag. Since the photospheric flux decreases to FIR almost strictly according to Planck's law, σ(W4) also gives a conservative estimate of the uncertainties of model fluxes at FIR. In the following analysis, we will incorporate these numbers as the uncertainties of model fluxes in the two WISE bands and all AKARI/FIS bands.

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2.3. Identification of Debris Disk Candidates

Our goal is searching for the IR excess from debris disks, while a debris disk is not the only source of the IR excess. So we will remove other IR excess sources from our sample. First, in some young O stars, significant IR excess may arise from gas free-free emission instead of from the debris disk. These stars generate strong ionized winds that produce strong IR and radio excesses. Thus, five O stars are excluded from our sample. Second, a Be star is a B-type star with prominent hydrogen emission lines in its spectrum and IR excess (Porter & Rivinius 2003). Both emission lines and excessive IR emission in Be stars are formed in circumstellar disks that are most likely ejected or stripped from the stars themselves. We rejected 12 Be stars based on SIMBAD classification. Third, we reject three objects including a star without reliable flux density of AKARI/FIS (none of the band has the quality flag = 3), a quasar, and a post-AGB star.

Finally, young stellar objects (YSOs) often harbor protoplanetary disks (Moór et al. 2006) and also display IR excesses. We will reject them according to the shape of their SEDs in the IR as follows. YSOs are classified observationally according to the shape of their SEDs in the IR between the K band (at 2.2 μm) and the N band (at 10 μm), defined as (Armitage 2007)

$$\begin{equation} \alpha _{\rm IR} = \frac{\Delta \log (\lambda F_\lambda)}{\Delta \log \lambda }, \end{equation} \tag{ 2 }$$

where α_IR > −1.5 is a strong indication for a YSO. In our sample, several stars have the YSOs' SED features as Class I (approximately flat or rising SED into mid-IR (α_IR > 0)) and Class II (falling SED into mid-IR (−1.5 < α_IR < 0)). Class I YSOs are typically younger and possess more massive disks than Class II objects. In principle, YSOs should have been removed from our selection of MS stars using the H–R diagram. However, stars would cross the MS belt on the H–R diagram when they evolve from the pre-main-sequence (PMS) to the zero-age-main-sequence (ZAMS) stars. Most of these stars are very close to the ZAMS, and only a small fraction may have massive planetary disks. According to our SED fitting, we reject 20 YSOs in total and list them in Table 1. In addition, we also purge another three stars (HIP 53911, HIP 77542, and HIP 23633) classified as YSOs in SIMBAD, although their IR slope does not meet above criteria. All these rejected stars are listed in Table 1. We retain a sample of 79 stars.

Table 1. List of Rejected Sources

HIP	AKARI/FIS Identification	Reason for Rejection
3401	0043182+615442	1
4023a	0051337+513424	4
5147	0105535+655820	2
13330a	0251319+674845	4
15984a	0325506+305559	4
16826	0336292+481134	2
17890	0349363+385902	3
19395a	0409164+304638	4
19720a	0413352+101240	4
19762b	0414129+281229	4
22910	0455460+303320	3
22925	0455593+303403	3
23143	0458465+295039	3
23428	0502065-712018	1
23633	0504502+264318	3
23734	0506086+585829	2
23873	0507494+302410	3
24552	0516006-094831	3
25253	0524009+245746	3
25258	0524079+022751	3
25299	0524426+014349	3
25793	0530272+251957	3
26295	0535587+244500	3
26451	0537385+210834	2
28582	0601597+163102	3
30089	0619582-103822	5
30800	0628177-130310	2
32349	0645085-164258	8
32677a	0648585-150849	4
32923	0651333-065751	2
36369	0729106+205450	1
37279	0739178+051322	8
53691	1059071-770138	3
53911	1101516-344214	3
54413	1108017-773912	3
56379	1133251-701146	2
58520	1200066-781135	2
60936	1229071+020309	6
63973b	1306360-494107	4
71352	1435303-420930	1
72685b	1451400-305312	4
77542	1549578-035515	3
77952b	1555094-632558	4
78034	1556019-660907	2
78317	1559283-402150	3
78594a	1602491-044922	4
78943b	1606579-274308	4
79080	1608344-390612	3
79476	1613116-222904	3
81624	1640176-235344	3
82747	1654450-365317	3
85792	1731503-495235	2
93975b	1908039+214151	4
94260	1911115+154717	3
97649	1950472+085209	8
101983	2040025-603307	8
104580	2111024-634106	7
105638	2123489-404203	1
106079	2129147+442027	2
111785	2238316+555006	2
112377b	2245378+415308	4

Notes. Column (1): Hipparcos identification. Column (2): AKARI/FIS identification. Column (3): Reason for rejection. 1. O star. 2. Be star. 3. Young stellar objects (YSOs) or PMS stars. 4. Contamination. 5. Post AGB star. 6. Quasar. 7. AKARI/FIS flux density is not reliable (Fqual = 1). 8. No FIR excess. ^aStars in nebula. ^bRejected by diffuse WISE images.

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In order to assess whether there is an excess IR emission in the rest of the sample, we calculate the significance of the excess to the stellar photospheric emission model in each AKARI/FIS band using the formula (Beichman et al. 2006; Moór et al. 2006)

$$\begin{equation} \protect \chi = \protect [\protect F_{{\rm IR}} - F_{{\rm phot}}\protect ] \protect / \sigma _{{\rm tot}}, \protect \end{equation} \tag{ 3 }$$

where F_IR is the measured flux density, F_phot is the predicted photospheric flux density, and σ_tot is the quadratic sum of the uncertainty of the measured flux density and the uncertainty of the predicted flux density in the specific band as

$$\begin{equation} \protect \sigma _{{\rm tot}} = \sqrt{\sigma _{{\rm IR}}^2 + \sigma _{{\rm phot}}^2}. \protect \end{equation} \tag{ 4 }$$

An object is considered as an excess candidate star when χ > 3.0 (Su et al 2006) in one or more of 65, 90, 140, or 160 μm bands. Applying this criterion, we identify 75 FIR excess stars in total in the AKARI/FIS database. Due to the shallow AKARI/FIS flux limit, only four of the Hipparcos stars were sufficiently bright enough to have their photospheres detected in the far-IR in the absence of a FIR excess. Among these 75 stars, 72 stars have high-quality 90 μm flux densities (fqual = 3). The other three are flagged as having unreliable 90 μm fluxes. Two of them are safely detected in 140 μm or 160 μm bands, indicating the presence of a cold disk; the third has reliable fluxes in both 65 and 140 μm and is a well-known bright debris source.

The MIR excesses from the WISE 22 μm and 12 μm are estimated in the same way. Among the 75 objects, 53 stars show excesses at 22 μm at more than the 3σ level (see Figure 3(b)) after considering the systematical uncertainty of 0.13 mag (Section 2.2). After considering the systematical uncertainty of 0.06 mag, 37 stars show excesses at 12 μm. The WISE magnitudes for these 75 objects are presented in Table 2.

Table 2. Photometry and Flux Density for All Sources

Name	Hipparcos		2MASS				WISE								AKARI/FIS
HIP	B	V	J	H	K	rdflg	w1	w2	w3	w4	w1sat	w2sat	w3sat	w4sat	65 μm	90 μm	140 μm	160 μm	Fqual	Offset
	(mag)	(mag)	(mag)	(mag)	(mag)		(mag)	(mag)	(mag)	(mag)	(%)	(%)	(%)	(%)	(Jy)	(Jy)	(Jy)	(Jy)		''
746	2.61	2.27	1.71	1.58	1.45	333	−0.88	−0.18	1.46	1.33	0.22	0.19	0.24	0.00	0.26	0.73	0.35	0.05	1311	3.1
4683	8.65	8.60	7.87	7.55	7.45	111	7.19	7.12	4.73	2.56	0.07	0.00	0.00	0.00	7.17	8.61	7.78	6.26	3333	3.8
4789	6.70	6.70	6.53	6.56	6.55	111	6.52	6.47	5.68	3.17	0.14	0.06	0.00	0.00	1.15	1.23	null	0.57	1311	11.1
7345	5.69	5.62	5.49	5.53	5.46	111	5.47	5.30	5.34	3.74	0.19	0.14	0.00	0.00	1.92	1.78	2.35	0.03	1311	2.7
7978	6.08	5.54	4.79	4.40	4.34	333	4.17	3.91	4.22	3.95	0.21	0.22	0.00	0.00	1.44	0.90	0.56	null	1311	7.0
8851	9.58	9.40	8.99	8.98	8.95	122	8.91	8.93	8.35	6.11	0.01	0.00	0.00	0.00	0.32	0.53	1.50	null	1311	8.4
10064	3.14	3.00	2.74	2.77	2.68	333	1.46	1.25	2.68	2.46	0.20	0.19	0.09	0.00	0.42	0.59	null	null	1311	4.3
10670	4.03	4.01	3.80	3.86	3.96	331	3.95	3.64	3.99	3.51	0.19	0.19	0.00	0.00	1.10	0.75	null	0.49	1311	6.2
11847	7.87	7.47	6.70	6.61	6.55	111	6.54	6.52	6.50	4.24	0.14	0.06	0.00	0.00	0.72	0.57	null	null	1311	5.2
13487	8.84	8.45	7.66	7.61	7.57	111	7.44	7.45	6.59	3.22	0.06	0.00	0.00	0.00	4.95	7.05	3.08	3.60	3311	5.3
14043	5.19	5.24	5.32	5.40	5.43	111	5.33	5.26	5.36	4.01	0.22	0.15	0.00	0.00	0.62	1.04	1.90	4.71	1311	14.8
16188	7.39	7.30	6.56	6.55	6.49	111	6.47	6.41	6.32	5.27	0.13	0.06	0.00	0.00	1.54	0.76	0.89	1.39	1311	18.3
17812	8.56	8.45	8.07	8.08	8.00	111	8.02	8.00	7.56	5.50	0.00	0.00	0.00	0.00	0.45	0.45	0.02	1.45	1311	8.3
17941	8.93	8.81	8.60	8.62	8.58	122	8.58	8.58	7.50	4.24	0.00	0.00	0.00	0.00	1.02	1.36	2.04	1.54	1311	12.2
19475	9.57	9.30	8.06	8.01	7.94	111	7.88	7.90	7.93	7.93	0.03	0.00	0.00	0.00	null	0.20	null	4.02	1113	9.4
20556	7.02	6.84	6.31	6.24	6.26	111	6.26	6.15	5.97	4.78	0.14	0.09	0.00	0.00	0.25	0.77	0.55	0.12	1311	3.6
20884	5.44	5.54	5.73	5.79	5.79	111	5.87	5.75	5.50	3.07	0.18	0.12	0.00	0.00	null	0.57	null	0.57	1311	18.2
21219	7.06	6.90	6.52	6.52	6.48	111	6.45	6.44	6.50	6.43	0.13	0.06	0.00	0.00	null	0.21	1.93	null	1131	5.7
21898	8.52	8.20	8.02	7.99	7.89	111	7.82	7.82	7.35	5.36	0.05	0.00	0.00	0.00	0.97	0.95	1.11	1.49	1311	16.9
22845	4.73	4.64	4.85	4.52	4.42	311	4.41	4.17	4.43	4.06	0.23	0.23	0.00	0.00	0.23	0.43	0.64	3.41	1311	8.1
23451	8.61	8.50	7.69	7.62	7.59	111	7.59	7.63	6.92	3.95	0.12	0.00	0.00	0.00	null	0.82	null	null	1311	4.0
24052	8.23	8.10	7.28	7.35	7.30	111	7.27	7.31	6.20	2.69	0.08	0.00	0.00	0.00	3.75	4.20	3.70	0.93	3331	9.9
26062	7.00	6.97	6.84	6.92	6.82	111	6.81	6.75	5.13	2.29	0.11	0.04	0.00	0.00	1.44	0.91	null	1.29	1311	4.1
27296	7.14	7.12	7.09	7.13	7.12	111	7.10	7.14	6.71	3.91	0.09	0.00	0.00	0.00	0.87	1.35	1.34	0.83	1311	5.0
27321	4.02	3.85	3.67	3.54	3.53	333	3.48	3.18	2.60	0.01	0.24	0.24	0.09	0.00	15.72	12.10	5.88	2.95	3331	4.2
32345	7.44	7.45	7.50	7.53	7.52	111	7.47	7.51	7.30	5.96	0.06	0.00	0.00	0.00	0.64	0.59	2.18	0.66	1311	10.5
36437	7.10	7.18	7.30	7.43	7.38	111	7.33	7.43	7.02	3.68	0.08	0.00	0.00	0.00	0.70	0.64	0.00	null	1311	11.2
36581	8.12	7.95	7.82	7.77	7.69	111	7.76	7.60	6.49	4.70	0.05	0.00	0.00	0.00	0.94	0.53	null	1.55	1311	7.7
40016	6.32	6.47	6.72	6.84	6.83	111	6.71	6.74	5.97	2.41	0.13	0.03	0.00	0.00	3.91	4.57	2.15	0.68	3311	3.5
40024	7.85	7.93	8.04	8.06	8.06	111	8.05	8.05	7.37	4.05	0.00	0.00	0.00	0.00	1.30	1.78	1.22	1.24	1311	4.1
40748	10.38	10.40	10.32	10.31	10.25	222	10.15	9.95	8.57	5.72	0.00	0.00	0.00	0.00	0.22	0.44	null	null	1311	13.2
41650	8.60	8.60	8.43	8.28	7.92	111	7.04	6.30	3.09	1.13	0.24	0.15	0.08	0.00	1.41	1.27	1.48	0.23	1311	5.9
44001	5.87	5.66	5.27	5.21	5.16	111	5.16	4.98	5.20	4.89	0.21	0.18	0.00	0.00	0.17	0.49	null	1.48	1311	6.3
45581	5.30	5.28	5.24	5.27	5.17	111	5.06	4.90	5.14	4.84	0.20	0.14	0.00	0.00	0.39	0.67	0.50	null	1311	11.8
46021	8.98	8.90	8.62	8.66	8.59	112	8.53	8.53	7.59	5.50	0.00	0.00	0.00	0.00	null	0.58	1.93	1.22	1311	8.6
48613	5.71	5.72	5.70	5.76	5.74	111	5.71	5.61	5.66	4.56	0.18	0.14	0.00	0.00	0.99	0.48	null	null	1311	18.3
53524	7.60	7.36	6.91	6.87	6.79	111	6.72	6.75	6.69	5.47	0.10	0.02	0.00	0.00	0.62	0.57	1.29	0.20	1311	2.7
55505	9.72	8.52	6.40	5.76	5.59	111	5.50	5.34	3.11	0.20	0.20	0.15	0.07	0.00	7.18	5.82	2.80	2.57	3311	8.5
57632	2.23	2.14	1.85	1.93	1.88	333	0.46	0.13	2.06	1.70	0.24	0.23	0.24	0.00	0.38	0.61	0.22	2.20	1311	7.3
57757	4.15	3.60	2.60	2.36	2.27	333	0.71	0.83	2.39	2.29	0.24	0.22	0.21	0.00	0.15	0.45	null	2.39	1311	15.8
60074	7.63	7.03	5.87	5.61	5.54	111	5.52	5.36	5.54	5.18	0.18	0.13	0.00	0.00	0.62	0.56	null	null	1311	9.4
61498	5.78	5.78	5.78	5.79	5.77	111	5.37	5.40	5.02	1.22	0.17	0.10	0.00	0.00	6.07	4.50	3.26	null	3311	8.9
65875	8.58	8.08	7.17	6.97	6.90	111	6.86	6.86	6.70	3.99	0.20	0.00	0.00	0.00	0.31	0.57	null	null	1311	6.7
73145	8.05	7.90	7.60	7.56	7.52	111	7.51	7.52	6.92	4.27	0.07	0.00	0.00	0.00	0.60	0.56	0.07	null	1311	5.4
74421	6.02	6.01	5.91	5.91	5.91	111	5.91	5.81	5.82	5.26	0.17	0.11	0.00	0.01	0.81	2.06	4.51	5.28	1331	16.4
76736	6.51	6.43	6.30	6.34	6.27	111	6.27	6.22	6.16	5.01	0.15	0.08	0.00	0.00	0.45	0.57	null	0.17	1311	10.4
76829	5.04	4.62	4.02	3.73	3.80	333	3.68	3.09	3.65	3.52	0.25	0.23	0.02	0.00	1.23	0.54	null	1.71	1311	9.0
77441	8.57	8.10	7.39	7.22	7.20	111	7.16	7.18	7.07	6.35	0.11	0.00	0.00	0.00	0.30	0.38	null	0.36	1311	5.7
79977	9.58	9.09	8.06	7.85	7.80	111	7.76	7.76	7.46	4.29	0.08	0.00	0.00	0.00	0.63	0.70	null	1.04	1311	6.9
80951	10.04	9.40	8.52	8.32	8.26	112	8.20	8.23	8.19	7.93	0.00	0.00	0.00	0.00	0.12	0.38	1.40	null	1311	6.9
81474	6.84	6.70	5.90	5.78	5.69	111	5.61	5.50	5.45	3.79	0.20	0.12	0.00	0.00	1.70	1.92	null	0.06	1311	12.5
81891	6.38	6.46	6.58	6.67	6.63	111	6.55	6.62	6.29	4.45	0.12	0.04	0.00	0.00	0.52	0.70	null	0.12	1311	8.5
82770	8.46	7.95	6.96	6.75	6.64	111	6.61	6.59	6.67	6.54	0.14	0.04	0.00	0.00	0.58	0.35	0.60	null	1311	15.7
83505	8.24	8.10	7.52	7.54	7.52	111	7.47	7.51	7.24	5.23	0.15	0.00	0.00	0.00	1.25	0.89	null	2.87	1311	4.0
85537	5.62	5.39	4.81	4.88	4.80	111	4.78	4.57	4.80	4.60	0.22	0.22	0.00	0.00	0.16	0.31	null	null	1311	10.1
86078	8.00	7.80	7.02	6.95	6.79	111	6.71	6.70	6.72	6.08	0.12	0.03	0.00	0.00	0.47	0.54	1.91	null	1311	19.1
87108	3.79	3.75	3.59	3.66	3.62	333	3.68	3.36	3.65	3.12	0.26	0.24	0.03	0.00	1.31	0.89	null	0.59	1301	5.7
87807	7.94	7.70	7.45	7.45	7.39	111	7.34	7.37	6.97	5.49	0.18	0.00	0.00	0.00	0.08	0.51	null	0.42	1311	6.0
88399	7.46	7.01	6.16	6.02	5.91	111	5.76	5.70	5.80	4.94	0.18	0.10	0.00	0.00	0.60	0.49	0.45	null	1311	4.7
88983	8.15	8.00	7.30	7.19	7.18	111	7.16	7.17	7.22	7.07	0.09	0.00	0.00	0.00	0.26	0.50	2.25	null	1311	18.3
90491	8.76	8.50	8.23	8.21	8.13	111	8.09	8.10	7.97	6.12	0.00	0.00	0.00	0.00	null	0.49	1.03	0.51	1311	4.5
91262	0.03	0.03	−0.18	−0.03	0.13	333	−2.03	−2.08	0.02	−0.16	0.31	0.31	0.30	0.00	6.58	6.20	4.05	3.22	3311	3.4
92800	6.80	6.80	6.53	6.54	6.50	111	6.42	6.42	6.17	4.05	0.13	0.04	0.00	0.00	2.71	2.55	2.19	3.02	3311	6.4
93000	7.37	7.15	6.63	6.61	6.58	111	6.54	6.46	6.05	4.16	0.13	0.05	0.00	0.00	1.17	1.80	0.78	null	1311	11.9
95270	7.52	7.04	6.20	5.98	5.91	111	5.89	5.81	5.89	3.95	0.18	0.11	0.00	0.00	1.71	1.46	1.24	1.23	1311	7.9
95619	5.64	5.66	5.67	5.66	5.68	111	5.68	5.56	5.61	4.58	0.21	0.13	0.00	0.00	0.45	0.73	0.07	null	1311	7.6
99273	7.66	7.18	6.32	6.09	6.08	111	6.06	5.88	6.00	4.06	0.16	0.07	0.00	0.00	1.22	0.59	1.48	0.15	1311	14.6
101612	5.04	4.75	4.28	4.02	4.04	333	4.06	3.58	4.04	3.87	0.24	0.22	0.00	0.00	null	0.53	null	0.37	1311	4.9
102761	8.01	7.97	7.89	7.93	7.95	111	7.92	7.95	7.13	4.06	0.03	0.00	0.00	0.00	1.66	1.91	1.59	0.01	1311	11.0
104354	8.37	8.31	8.12	8.13	8.12	112	8.10	8.13	7.21	4.70	0.00	0.00	0.00	0.00	0.10	0.54	null	null	1311	7.3
111214	9.16	8.90	8.58	8.64	8.62	122	8.59	8.62	8.19	6.50	0.00	0.00	0.00	0.00	0.20	0.32	1.12	0.30	1311	12.8
111429	6.88	7.00	7.19	7.27	7.29	111	7.23	7.34	7.38	6.68	0.08	0.00	0.00	0.00	0.10	0.93	2.63	1.26	1311	15.2
113368	1.25	1.17	1.04	0.94	0.94	333	−1.47	−0.75	1.11	0.79	0.31	0.28	0.29	0.00	8.30	10.27	7.71	4.66	3131	4.9
114189	6.25	5.98	5.38	5.28	5.24	111	5.19	5.04	5.21	4.85	0.20	0.16	0.00	0.00	1.12	0.48	0.26	3.48	1311	4.8
118289	7.13	7.17	7.18	7.26	7.26	111	7.18	7.26	6.22	3.64	0.06	0.00	0.00	0.00	1.13	1.07	1.09	null	1311	6.3

Notes. Column (1): Hipparcos identification. Column (2): B magnitude. Column (3): V magnitude. Column (4): J magnitude. Column (5): H magnitude. Column (6): K magnitude. Column (7): Column Read flag. Column (8): WISE W1 magnitude. Column (9): WISE W2 magnitude. Column (10): WISE W3 magnitude. Column (11): WISE W4 magnitude. Column (12): Saturated pixel fraction, W1. Column (13): Saturated pixel fraction, W2. Column (14): Saturated pixel fraction, W3. Column (15): Saturated pixel fraction, W4. Column (16): AKARI/FIS 65 μm flux density. Column (17): AKARI/FIS 90 μm flux density. Column (18): AKARI/FIS 140 μm flux density. Column (19): AKARI/FIS 160 μm flux density. Column (20): Flux density quality flag in AKARI/FIS 4 bands: 3 = High quality (the source is confirmed and flux is reliable); 2 = The source is confirmed but flux is not reliable (see FLAGS); 1 = The source is not confirmed; 0 = Not observed (no scan data available). Column (21): AKARI/FIS position offset.

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We have identified a sample of 75 stars with debris disks. In this section, we will study the properties of host stars and debris disks. The stellar properties include magnitude, color, and location on the H–R diagram, as well as those derived from the SED fitting in the previous section. The properties of debris disks are derived by using the parameters obtained in modeling the IR excesses in AKARI/FIS and WISE data.

Previous studies suggested that debris disks are optically thin and usually consist of a narrow ring (Backman & Paresce 1993) in thermal equilibrium with the stellar radiation field. Therefore, the IR excess is usually modeled as a single-temperature blackbody (Kim et al. 2005; Bryden et al. 2006; Rhee et al. 2007). There are two free parameters in the fit, blackbody temperature and its normalization. To fully determine the model parameters, excesses in at least two bands are needed, while with more data points, we can get a best fit by minimizing χ². Therefore, according to the number of bands with detected FIR and MIR excesses (AKARI/FIS 4 bands and WISE 12 μm and 22 μm), we further divide the IR excess sample into two groups: IR excess in a single band (Group I) and excesses in two or more bands (Group II). Note that both Groups I and II should show excess in at least one AKARI/FIS band. Only for sources in Group II can the dust temperature be fully determined for the single-temperature dust model, while in Group I, by combining AKARI/FIS data with the upper limits at the WISE 22 μm, we can derive an upper limit on the dust temperature. Among the 75 debris disk candidates, the majority (55)⁴ are in Group II. In passing, we note that 11 objects are detected in 2 or more AKARI/FIS bands. They are brighter at 90 μm on average, and a significant fraction (9/11) of these sources displays MIR excess. Similarly, bright sources are more likely to show 22 μm excesses.

3.1. Stellar Properties of Debris Disk Hosts

3.2. Disk Properties

By fitting the IR excess flux densities, we derive the dust temperature and the fraction of the stellar luminosity reprocessed by dust. By combining with additional stellar parameters, we can estimate the dust location and other quantities. The inferred basic disk properties are listed in Table 3. In the following subsections, we describe the method and results in detail.

Table 3. Star Basic Properties and Dust Basic Properties of Our Sample Sources (Group II)

HIP	HD	Distance(pc)	Teff	logg	E(B − V)	Td (K)	Rd (AU)	Md(M⊕)	fd	Sp.Type	References
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
4683a	232344	446.4	10000	4.0	0.200	53	363	2.22e+02	1.53e-02	B5	1
4789	5839	357.1	11000	4.0	0.093	106	145	3.59e+00	1.55e-03	B9	1, 4
7345	9672	61.3	9500	4.5	0.028	77	60	3.05e-01	7.65e-04	A1V	1, 2, 4, 10
8851	...	411.5	10500	4.0	0.200	136	31	5.47e-02	4.89e-04	B8	...
11847	15745	63.7	8000	4.5	0.178	90	22	7.46e-02	1.36e-03	F0	2, 5, 10, 11
13487a	17706	261.1	10000	4.0	0.200	41	367	1.55e+02	1.05e-02	B8	1
14043	18537	243.9	20000	4.0	0.138	81	701	2.54e+00	4.71e-05	B7V	...
16188	21377	353.4	8750	4.0	0.192	69	250	5.80e+00	8.43e-04	A0	...
17812	23777	393.7	10000	4.0	0.157	79	128	2.92e+00	1.61e-03	B9	...
17941	23861	331.1	9500	4.5	0.064	86	63	5.06e+00	1.14e-02	A0	...
20556	27636	194.9	9750	4.0	0.200	75	154	1.43e+00	5.48e-04	A2	...
20884	28375	118.1	13000	4.0	0.000	119	67	1.46e-01	2.96e-04	B3V	1
21898	29733	537.6	8250	4.5	0.000	70	169	1.63e+01	5.17e-03	A0	...
23451	32297	112.1	8500	4.0	0.200	96	23	2.75e-01	4.56e-03	A0	2, 10
24052a	33002	159.2	10000	4.0	0.200	45	214	1.76e+01	3.48e-03	B9	...
26062	36546	100.0	10000	4.0	0.048	134	18	1.33e-01	3.40e-03	B8	...
27296	38402	325.7	15000	4.0	0.134	85	247	5.18e+00	7.69e-04	B8	...
27321	39060	19.3	8500	4.5	0.010	120	16	8.08e-02	2.85e-03	A3V	1, 2, 6, 7, 10, 12, 13
32345	48808	454.5	10500	4.0	0.002	67	272	8.01e+00	9.86e-04	B9	...
36437	59543	490.2	14000	4.0	0.034	98	219	4.13e+00	7.84e-04	B3IV/V	...
36581	59509	666.7	8750	4.5	0.011	93	142	7.12e+00	3.22e-03	F8	...
40016a	68478	500.0	16000	4.0	0.008	37	2500	3.48e+02	5.07e-04	B3IV	1
40024	68496	450.5	11500	4.0	0.003	82	158	1.43e+01	5.18e-03	B6V	...
40748	...	763.4	10000	4.0	0.036	86	71	7.56e+00	1.35e-02	B4	...
41650	72106	288.2	9250	4.0	0.101	194	12	8.48e-01	4.73e-02	A0IV	1
46021	81335	458.7	9750	4.0	0.098	77	112	5.23e+00	3.78e-03	A0III/IV	...
48613	86087	97.8	10000	4.0	0.000	83	80	1.79e-01	2.50e-04	A0V	4
53524	95086	91.6	9250	4.5	0.169	70	58	2.79e-01	7.41e-04	A8III	2, 4
55505	98800	46.7	4750	4.0	0.184	139	4	1.67e-01	6.16e-02	K4V	2
61498	109573	67.1	10000	4.5	0.001	101	36	5.26e-01	3.68e-03	A0V	2, 3, 10, 13
65875	117214	97.1	7250	4.5	0.154	95	21	1.52e-01	2.90e-03	F6V	...
73145	131835	111.1	9250	4.5	0.096	97	25	1.86e-01	2.53e-03	A2IV	2, 10
74421	133981	260.4	10250	4.0	0.053	27	1851	2.25e+02	5.97e-04	B8/B9III	...
76736	138965	77.3	9500	4.5	0.030	75	55	1.68e-01	4.95e-04	A5V	2
77441	141133	117.0	7500	4.5	0.109	63	55	4.03e-01	1.18e-03	F2/F3V	...
79977	146897	131.8	7250	4.5	0.190	87	23	4.17e-01	6.77e-03	F2/F3V	4
81474	149914	165.0	10000	4.0	0.200	78	144	2.32e+00	1.01e-03	B9.5IV	1
81891	150638	240.4	12000	4.0	0.001	87	155	1.43e+00	5.37e-04	B8V	...
83505	154002	342.5	10000	4.0	0.200	71	175	5.86e+00	1.74e-03	B9.5III	...
86078	159525	317.5	8250	4.0	0.197	62	215	4.43e+00	8.70e-04	A0	...
87807	163422	207.9	11750	4.0	0.200	74	129	1.11e+00	6.04e-04	B9	...
88399	164249	46.9	7750	4.5	0.194	76	29	5.16e-02	5.54e-04	F5V	2, 5, 10, 12
90491	170116	117.5	8250	4.5	0.008	67	35	4.41e-01	3.13e-03	A0	...
91262	172167	7.8	10000	4.0	0.022	65	146	2.45e-02	1.04e-05	A0V	1, 2, 6, 7, 13
92800	175427	225.7	10000	4.0	0.095	72	174	7.04e+00	2.10e-03	A0	1
93000	175623	354.6	10000	4.0	0.200	75	243	1.09e+01	1.68e-03	B8II/III	...
95270	181327	50.6	6500	4.0	0.001	78	22	1.68e-01	3.05e-03	F5/F6V	2, 10, 12
95619	182681	69.1	10250	4.0	0.009	76	72	1.66e-01	2.90e-04	B8/B9V	2, 10
99273	191089	53.5	6500	4.0	0.001	91	16	5.22e-02	1.82e-03	F5V	2, 9, 10
102761	198739	431.0	18000	4.0	0.194	81	334	1.45e+01	1.18e-03	B8	...
104354	201469	555.6	14000	4.0	0.184	98	185	3.68e+00	9.74e-04	B9	...
111214	213632	393.7	11500	4.0	0.200	69	160	3.07e+00	1.09e-03	B9	...
111429	213976	289.9	14000	4.0	0.015	53	462	9.71e+00	4.14e-04	B1.5V	...
113368	216956	7.7	8750	4.0	0.008	54	107	6.30e-02	4.98e-05	A3V	1, 2, 5, 6, 7, 8, 13
118289	224648	300.3	18000	4.0	0.142	103	195	2.24e+00	5.32e-04	B9	1

Notes. Column (1): Hipparcos identification. Column (2): HD numbers. Column (3): Distance. Column (4): Effective temperature. Column (5): Surface gravity. Column (6): E(B − V). Column (7): Dust temperature. Column (8): Dust location. Column (9): Total dust mass(M_⊕). Column (10): Dust fractional luminosity. Column (11): Spectral type. Column (12): References – (1) Oudmaijer et al. 1992; (2) Rhee et al. 2007; (3) Koerner et al. 1998; (4) Chen et al. 2006; (5) Decin et al. 2003; (6) Habing et al. 1999; (7) Habing et al. 2001; (8) Su et al. 2006; (9) Carpenter et al. 2008; (10) Moór et al. 2006; (11) Moór et al. 2011; (12) Rebull et al. 2008 (13) Rieke et al. 2005. ^aSED fitting with two blackbody model.

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3.2.1. Dust Temperature

We fit the excessive flux densities in the AKARI/FIS and WISE bands with a single-temperature blackbody model as described, convolved with the response functions of the corresponding filters. In the case of single band excess (Group I, 20 stars in total), we derive a maximum temperature by combining the excess AKARI/FIS flux with the upper limits at 22 μmand the normalization of blackbody radiation at the maximum temperature. Note that this normalization is usually higher than the one assuming that the blackbody peaks at the detected IR band, as in Rhee et al. (2007). In the case of two band excesses, we can fit the blackbody solution directly to determine the temperature and normalization. We estimate the uncertainty of a parameter by using χ² as a function of the parameter. We adopt Δχ² = 2.7 in the error estimate, i.e., at 90% confidence level for one interesting parameter. In the case of more than two band excesses (38 objects, including 37 stars with 12 μm excess; 30 stars have three band excesses and 8 stars have four or more band excesses), the best-fit parameters are determined by minimizing χ², and again the uncertainties of parameters are given at Δχ² = 2.7. The typical uncertainty in the dust temperature is about 3 K. We do not use IRAS fluxes because these fluxes may suffer from contaminations, in particular, for the objects beyond 100 pc, where the contamination of cirrus is severe due to poor spatial resolution of IRAS.

In most cases, a single-temperature blackbody usually gives an acceptable fit to the data for sources with multi-band excesses. Examples of SED fitting are shown in Figure 4. We consider minimum χ² > 6.7 for three band excesses and χ² > 9.2 for four band excesses to be unacceptable (at <1% probability). Using these criteria, 15 stars require a more complicated model, including 11 stars with excesses in three bands and 4 stars with excesses in four or more bands. This indicates either multi-temperature components or a non-blackbody nature of the dust grains. We use a double-blackbody model to fit the SED of the four stars with excesses in four or more bands (Figure 5). The temperatures for the two components are (206, 54) K, (110, 41) K, (107, 45) K, and (105, 37) K, respectively. Three of them are clustered around (100, 40) K and the other around (∼200, 50) K. The star with a warm component (∼200 K) has a fairly large ratio of excesses at W3 and W4, so the presence of a warm component is independent of modeling, while the other three show rather steep spectrum between W3 and W4. The temperatures of the warm components are similar to that of grains in the asteroid belt of our solar system, while that of the cold components are similar to that in the Kuiper Belt. For 14 stars with three band excesses that cannot be well fitted by a single-temperature blackbody model, it is insufficient to constrain the temperatures in a dual blackbody model. However, according to the excess flux ratio between W3 and W4, we speculate that about seven stars may have a warm component.

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Note that weak 12 μm excess does not significantly affect the fit to the cold component. Therefore, we will focus only on the cold component in the rest of this paper. The best-fitted T_d is listed in column (7) in Table 3. The distribution of T_d is shown in Figure 6(b). Dust temperatures are falling in the range of 27–194 K with a median value of 78 K. The dust temperatures of the disk correspond to the peak of blackbody emission from 26 μm to 189 μm.

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3.2.2. Fractional Luminosity

Fractional luminosity f_d is defined as the ratio of IR luminosity of the debris disk to that of the star, frequently used to characterize the effective optical depth of the disk,

$$\begin{equation} f_{\rm d} = L_{\rm ir}/ L_\star \protect, \protect \end{equation} \tag{ 5 }$$

where L_ir is the IR luminosity estimated by the fitted IR blackbody model. The stellar luminosity L_⋆ is calculated from the best-fit Kurucz model. The uncertainties of f_d can be estimated by a combination of the uncertainties in the temperatures $\sigma _{T_d}$ and normalization. The typical fractional uncertainty of f_d is 0.14 for our sample.

We plot the distribution of the f_d in Figure 6(c). Our sample spans a large range of f_d, 1.04 × 10⁻⁵ < f_d < 0.06, with a median value of 1.18 × 10⁻³. Limited by the sensitivity of the AKARI/FIS, the distribution itself should not be taken too seriously because disks with low f_d can be detected by AKARI/FIS only for very bright nearby stars, resulting in a distribution strongly biased to the higher f_d.

3.2.3. Dust Location, Dust Mass

With the assumption that the debris disk is optically thin in thermal equilibrium with the stellar radiation field, the temperature of a dust grain with a given chemical composition and grain size depends on the radial distance to the central star only (Kim et al. 2005). Assuming that the dust is located in a narrow ring between R_d − dR_d and R_d + dR_d, one can write the radius of dust ring R_d with the formula (Backman & Paresce 1993)

$$\begin{equation} R_{d} = (278 / T_{d}) ^{2} (L_\star / L_\odot) ^{0.5}\protect. \protect \end{equation} \tag{ 6 }$$

Because this formula assumes that the dust is blackbody-like, the resulting R_d corresponds to a minimum possible radius (Moór et al. 2011). The uncertainties of R_d are estimated from the error propagation of the uncertainties of temperatures $\sigma _{T_d}$. This formally gives a typical error of 10% in R_d. Figure 6(d) shows the distribution of the dust location R_d.

The total mass M of dust can be written with the formula (Rhee et al. 2007)

$$\begin{equation} M_{d} = (4 \pi a^{3}/3) \rho N\protect, \protect \end{equation} \tag{ 7 }$$

where N is the total number of grains in the disk and a and ρ are the mass weighted average radius and density of grains, respectively. For an optically thin dusty ring/shell of characteristic radius R,

$$\begin{equation} f_{d} = N\pi a^{2}/\left(4\pi R_{d}^{2}\right). \end{equation} \tag{ 8 }$$

Then,

$$\begin{equation} f_{d}/M_{d} \varpropto1/\left(\rho aR_{d}^{2}\right). \end{equation} \tag{ 9 }$$

If the characteristic grain size and density do not vary much in different debris disks, then one expects f_d/M_d to vary as the inverse square power of the disk radius, R_d (Rhee et al. 2007). The slope is a constant, which can be derived from the disks that their masses were derived from submillimeter data. We use the slope from Rhee et al. (2007; see Figure 5). Therefore, we can change the equation to

$$\begin{equation} M_{d}=f_{d} \left(R_{d}^{2}/9.12\right) M_\oplus \protect, \protect \protect \protect \end{equation} \tag{ 10 }$$

where f_d and R_d are taken from column (10) and column (8) in Table 3, respectively. Then the calculated dust mass is listed in column (9) in Table 3. Noting that we have adopted several assumptions in deriving dust mass, which are only valid statistically, the dust mass is only a rough estimate for an individual object.

An effective way of characterizing the sample is to make a comparison with other samples in the literature. A similar one is the IRAS debris disk sample, which was constructed by cross-correlating the Hipparcos MS star catalog with the IRAS Point Source Catalog (PSC) and Faint Source Catalog (FSC; Rhee et al. 2007). The sample consists of 146 stars within 120 pc of the Earth that show excess emissions at 60 μm. The distance limit is so set to avoid possible heavy contamination arising from interstellar cirrus or star-forming regions. Most of these stars belong to early types, from late-B- to early-K-type stars, similar to our sample. Despite the similar sensitivity of IRAS at 60 μm band and AKARI/FIS at 90 μm, only 27 stars in Rhee et al. are similar to ours, while 35 stars in total are within 120 pc of our sample.

To understand what causes the difference, we search the flux density at 60 μm of Rhee et al. 's sample from the IRAS PSC and FSC with a matching radius of 45'' as described in Rhee et al. (2007). Figure 7 shows that the IRAS flux at 60μm and AKARI flux at 90 μm are fairly well correlated for those detected in both bands (29 in total, including 27 in our sample and 2 PMS stars rejected from our sample mentioned in Section 2.3) and within 120 pc of the Earth. A logarithm linear fit to the data yields a best fit of log f_90μ m = 0.90log f_60μ m − 0.08. The ratio of the 2 fluxes is certainly dependent on the disk temperature, but with only 29 data points in hand, we will not explore this further. In our sample, 27 stars beyond 120 pc have an IRAS detection. For these stars, the flux ratios between IRAS 60 μm and that of AKARI/FIS 90 μm are substantially higher than those of nearby stars, especially for sources with f_60μ m > 1 Jy. This is likely caused by source contamination in IRAS. With a factor of more than four improvement in the spatial resolution, the contamination is greatly reduced in the AKARI/FIS flux.

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We examine these sources that appear only in one sample in detail. Nine stars within 120 pc are included in our sample, but not in Rhee et al. (2007). Five of them (HIP 10064, HIP 20884, HIP 26062, HIP 48613, and HIP 57757) have IRAS detections. HIP 57757 was rejected by Rhee as a non-IR excess star. Four stars are not in the rejected source table of Rhee et al. HIP 20884 and HIP 26062 were excluded due to the spectral-type cut in Rhee et al. HIP 10064 and HIP 48613 were reported to show an FIR excess (Oudmaijer et al. 1992; Chen et al. 2006), while the remaining four (HIP 65875, HIP 77441, HIP 88983, and HIP 90491) do not have available IRAS data. The AKARI/FIS 90 μm flux densities of these 4 stars are in the range from 0.4 to 0.7Jy. Adopting the above relation between 90 and 60 μ m for sources in common, the 60 μ m flux is expected to be 0.4–0.8 Jy. HIP 88983 and HIP 90491 are in the "IRAS Faint Source Catalog Rejects" with a 60 μ m flux of 0.33 Jy and 0.28 Jy with fqual = 2 and fqual = 1, respectively. This suggests that these sources have fainter 60 μ m fluxes than expected, which indicates cool debris disks. To produce a flux ratio of 0.6 between 60 and 90 μ m, the blackbody temperature would be about 50 K. At this temperature, flux ratios of 140 and 160–90 μ m are about 0.9 and 0.7, so the expected 140 and 160 μ m flux is below the detection limits in both bands, consistent with no detections in either band. The other two stars may have similar situations. Note that two of the debris disk candidates in the sample that have a firm flux only at 140 or 160 μ m are likely even cooler.

On the other hand, most sources (119/146) in Rhee et al. 's sample are not in ours. Most of these sources (113/119) have a flux f_60μ m < 0.63Jy, and it is not surprise that they are undetected by AKARI/FIS (red dots in Figure 7). According to the relation between f₉₀ and f₆₀, we expect f_90μ m < 0.55 Jy, which is below the formal flux limit of the AKARI. Thus the non-detection of these sources may be entirely due to the shallowness of the AKARI/FIS survey. Six bright IRAS stars are not in our final sample. Among them, the two brightest stars (HIP 53911 and HIP 77542) are actually detected by AKARI/FIS  but rejected as PMS according to the SIMBAD classification. We checked the other four stars and found no matching sources in the AKARI/FIS catalog, even at a larger matching radius.

For comparison, we overplot the disk parameters of the IRAS sample (Table 2 of Rhee et al. 2007) in Figures 6(b)–(d). Only sources with a fitted temperature, i.e., detected in more than one IRAS band, are shown. Our sample is distributed in a relatively narrower temperature range than the IRAS sample. However, as we have discussed above that four stars in our sample without available IRAS data may have very low temperatures, then this difference of temperature distribution between two samples may be not real. Our sample tends to have larger excesses and to possess more distant disks due to the different flux limits and the distance cut used in selection of the sample.

It should be cautioned that both dust temperature and normalization in Rhee et al. (2007) is based solely on IRAS, which has much poorer sensitivity in the MIR in comparison with WISE. Therefore, the dust temperature for a large fraction of objects in their sample could not be determined and were artificially assigned to 85 K so that the peak emission is at 60 μm. Even for those objects with multi-band IRAS detections, the dust temperatures were less well determined than in this paper.

Finally, a total of 43 stars were already reported in literature (notes in Table 3), so 32 stars are reported to have IR excesses for the first time in this paper. Most of them are located at a distance more than 120 pc from the Earth, but are relatively very luminous. As Kalas et al. (2002, p. 1002) pointed out, "Pleiades-like dust detected around the star is capable of producing the FIR emission rather than the Vega phenomenon." HIP 78594 (Table 1, marked with "a"), which was rejected by Moór et al. (2006), is such a star. So these 32 new IR excess stars need to be further checked out by coronagraphic optical observations to confirm whether debris disks are responsible for the IR excesses.

In this paper, we cross-correlate the AKARIBSC with the Hipparcos MS star catalog using a matching radius adapted to the local stellar surface density and yield a sample of 136 FIR detected stars (at >90% reliability) at least in one band. After rejecting 57 stars classified as young stellar objects, PMS stars and other types of stars with known dust disks or with potential contaminations, we obtain a sample of 75 candidate stars with debris disks and 4 stars without FIR excess. The stars in the sample span from B to K types, with only two G-type and 1 K-type stars.

With the shallow limit of AKARI/FIS, the survey can only recover the brightest debris disks. This represents a unique sample of luminous debris disks that are derived uniformly from an all-sky survey with a spatial resolution a factor of two better than the previous survey by IRAS. This sample is also complementary to the deep, small area surveys or deep surveys of nearby stars as already carried out with Spitzer and ISO that find mostly faint debris systems. Moreover, by collecting the IR photometric data from other public archives, 55 stars have IR excesses in more than one band, allowing an estimate of the dust temperature. We fit a blackbody model to the broadband SEDs of these stars to derive the statistical distribution of the disk parameters. Four objects with four or more band excesses can be fitted by a double-blackbody model. Three of them are clustered around (100, 40) K, and the other around (∼200, 50) K.

We thank the anonymous referee for comments that improved the paper. This work is supported by the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences, grant No. XDB09000000. This work is based on observations with AKARI, a JAXA project with the participation of ESA and makes use of data products from Hipparcos Catalogs (the primary result of the Hipparcos space astrometry mission, undertaken by the European Space Agency), 2MASS (a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology), and WISE (a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology). This work makes use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research makes use of ATLAS9 model and the SIMBAD database, operated at CDS, Strasbourg, France.