Global properties of the light curves of magnetic, chemically peculiar stars as a testbed for the existence of dipole-like symmetry in surface structures

TL;DR

This study investigates the surface structures of magnetic, chemically peculiar stars, revealing that their chemical spots do not align with magnetic field topology, challenging existing theories about magnetic influence on surface features.

Contribution

It provides the first large-scale analysis linking photometric spot distribution to magnetic field topology, using observational data and simulations to challenge current assumptions.

Findings

Observed light curves differ from dipole-based simulations

Chemical spot distribution does not follow magnetic field topology

Magnetic fields may play a subsidiary role in surface structure formation

Abstract

Magnetic, chemically peculiar stars are known for exhibiting surface abundance inhomogeneities (chemical spots) that lead to photometric and spectroscopic variability with the rotation period. It is commonly assumed that the surface structures are causally connected with the global magnetic field that dominates the photospheric and subphotospheric layers of these stars. As a rule, the observed magnetic fields show a simple dipole-like geometry, with the magnetic axis being noncollinear to the rotational one. The present study aims at detecting underlying patterns in the distribution of photometric spots in a sample of 650 magnetic, chemically peculiar stars and examines their link to the magnetic field topology. Photometric time-series observations from the ASAS-3 archive were employed to inspect the light-curve morphology of our sample stars and divide them into representative classes described using a principal component analysis. Theoretical light curves were derived from numerous simulations assuming different spot parameters and following the symmetry of a simple dipole magnetic field. These were subsequently compared with the observed light curves. The results from our simulations are in contradiction with the observations and predict a much higher percentage of doublewave light curves than is actually observed. We thereby conclude that the distribution of the chemical spots does not follow the magnetic field topology, which indicates that the role of the magnetic field in the creation and maintenance of the surface structures may be more subsidiary than what is predicted by theoretical studies.

Tables

Table 1. Table 1: Classification of light curves. SW = single wave, DW = double wave, n = number of local minima in the light curve.

Type	Conditions		n
symmetric SW	$\left|A_1\right|>3\delta A_1$		1
symmetric DW	$\left|A_2\right|>3\delta A_2$		2
asymmetric SW	$\left|A_1\right|>3\delta A_1$	$\left|A_3\right|>3\delta A_3$	1
asymmetric DW	$\left|A_2\right|>3\delta A_2$	$\left|A_3\right|>3\delta A_3$	2
low-quality data	all other data

Table 2. Table 2: Simulation results for all studied cases. The columns describe, respectively, the spot type (two dark spots vs. one dark spot and one spot of random opacity), the angular radius of the spots α 𝛼 \alpha , the occurrence rate of double-wave light curves, and the maximum values for the effective semi-amplitude A 𝐴 A . Values of the occurrence rate of the double-wave light curves are given with a left limit case that includes all 1000 simulation runs and a right limit case where only the 500 simulations with the highest resulting values of A 𝐴 A are taken into account.

Spot type	$\alpha$ [rad]	Rate [%]	$A_{\max }$ [mag]
completely dark	0.3	74-83	0.11
completely dark	0.7	79-86	0.52
completely dark	1.2	87-95	1.00
partially dark	0.7	74-88	0.62

Table 3. Table 3: Fit parameters and ephemerides of the 650 mCP stars. From left to right, the columns denote: the object identification (HD number or other conventional ID); the parameters A 1 subscript 𝐴 1 A_{1} , A 2 subscript 𝐴 2 A_{2} , and A 3 subscript 𝐴 3 A_{3} with their errors δ ​ A 1 𝛿 subscript 𝐴 1 \delta A_{1} , δ ​ A 2 𝛿 subscript 𝐴 2 \delta A_{2} , and δ ​ A 3 𝛿 subscript 𝐴 3 \delta A_{3} ; the standard deviation σ 𝜎 \sigma derived from Eq. 1 ; the period value P 𝑃 P and time of maximum light M 0 subscript 𝑀 0 M_{0} taken from Bernhard et al. ( 2015 ) and Hümmerich et al. ( 2016 ) ; and the wave number n 𝑛 n , which indicates (1) single-wave or (2) double-wave character of the light curve.

Star	$A_1$	$A_2$	$A_3$	$\delta A_1$	$\delta A_2$	$\delta A_3$	$\sigma$	P	$M_0-2450000$	n
	[mag]	[mag]	[mag]	[mag]	[mag]	[mag]	[mag]	[d]	[d]
HD10081	0.0004	-0.0129	-0.0027	0.0006	0.0006	0.0007	0.0132	1.570	2190.56	2
HD26726	-0.0301	-0.0010	-0.0008	0.0009	0.0009	0.0018	0.0151	5.382	1902.60	1
HD30898	-0.0154	-0.0004	0.0007	0.0008	0.0008	0.0016	0.0109	0.782	2185.79	1
HD35177	-0.0103	-0.0036	0.0004	0.0007	0.0007	0.0007	0.0093	0.528	2670.60	2
HD36997	-0.0119	-0.0039	-0.0004	0.0008	0.0008	0.0010	0.0134	6.007	3101.50	2
HD37189	-0.0030	-0.0105	0.0066	0.0006	0.0006	0.0006	0.0124	2.829	2115.90	2
HD37713	-0.0092	-0.0026	-0.0044	0.0008	0.0008	0.0009	0.0126	1.501	1914.64	1
HD38366	-0.0266	-0.0044	-0.0098	0.0011	0.0010	0.0013	0.0128	0.625	4143.68	1
HD38698	-0.0146	-0.0017	0.0053	0.0007	0.0007	0.0010	0.0106	3.164	2690.64	1
HD39635	-0.0188	-0.0051	0.0087	0.0013	0.0014	0.0014	0.0189	3.966	2752.51	1
HD42382	-0.0168	0.0005	-0.0016	0.0009	0.0009	0.0022	0.0140	5.928	2921.90	1
HD42695	-0.0090	0.0005	-0.0011	0.0007	0.0007	0.0018	0.0111	1.069	5148.78	1
HD44038	-0.0156	-0.0049	0.0008	0.0010	0.0010	0.0011	0.0162	0.690	3029.75	1
HD44290	-0.0065	-0.0080	-0.0006	0.0006	0.0006	0.0006	0.0098	1.715	2032.48	2
HD44456	0.0128	0.0106	-0.0031	0.0009	0.0008	0.0008	0.0120	3.893	2243.73	2
HD291674	-0.0088	-0.0034	0.0017	0.0009	0.0010	0.0011	0.0142	2.731	3457.57	1
HD258583	-0.0286	-0.0049	0.0041	0.0007	0.0008	0.0011	0.0110	10.312	2671.60	1
HD45931	-0.0121	-0.0107	-0.0094	0.0009	0.0008	0.0008	0.0117	1.927	2199.82	2
HD46234	-0.0082	-0.0018	-0.0041	0.0008	0.0008	0.0009	0.0121	4.694	1924.60	1
HD47026	-0.0087	-0.0109	-0.0046	0.0009	0.0008	0.0008	0.0141	1.280	2143.88	2
HD46739	-0.0166	-0.0003	-0.0036	0.0007	0.0007	0.0014	0.0125	1.111	3366.80	1
HD47714	0.0001	-0.0174	-0.0005	0.0007	0.0007	0.0007	0.0144	9.391	2249.70	2
HD48729	-0.0056	-0.0120	0.0099	0.0007	0.0007	0.0007	0.0134	1.892	2963.74	2
HD263361	-0.0286	-0.0121	0.0004	0.0011	0.0011	0.0013	0.0170	88.900	2715.50	2
HD263582	-0.0215	-0.0159	0.0003	0.0012	0.0012	0.0012	0.0168	2.092	2740.48	2
HD49686	-0.0104	-0.0100	0.0048	0.0008	0.0008	0.0008	0.0154	3.965	1929.63	2
HD49479	-0.0040	-0.0142	0.0075	0.0012	0.0012	0.0013	0.0173	7.388	2255.70	2
HD289186	-0.0130	0.0013	-0.0028	0.0012	0.0012	0.0038	0.0139	1.656	2654.67	1
HD50221	-0.0085	-0.0040	0.0055	0.0007	0.0007	0.0007	0.0110	1.974	1938.64	1
HD50540	-0.0169	-0.0072	-0.0119	0.0011	0.0011	0.0010	0.0162	1.554	1877.76	1
HD50391	-0.0086	-0.0011	-0.0012	0.0010	0.0010	0.0014	0.0157	1.183	3405.66	1
HD50461	-0.0093	-0.0036	0.0085	0.0010	0.0010	0.0009	0.0131	0.894	3411.76	1
HD50829	-0.0348	-0.0155	0.0008	0.0007	0.0007	0.0007	0.0141	3.414	1935.54	2
HD50855	-0.0244	-0.0016	0.0011	0.0015	0.0015	0.0026	0.0252	2.239	2754.52	1
HD50895	-0.0242	-0.0037	0.0039	0.0008	0.0008	0.0012	0.0132	3.590	2911.85	1
HD51088	-0.0056	-0.0059	-0.0112	0.0010	0.0009	0.0008	0.0127	1.653	3445.55	2
HD51031	-0.0319	-0.0029	-0.0001	0.0007	0.0007	0.0011	0.0114	2.364	2987.76	1
HD51203	-0.0110	-0.0052	-0.0066	0.0009	0.0009	0.0009	0.0172	6.675	3389.70	1
HD51307	-0.0131	-0.0055	-0.0078	0.0007	0.0007	0.0007	0.0128	4.017	3759.63	1
HD51172	-0.0040	-0.0181	-0.0052	0.0008	0.0009	0.0009	0.0137	2.479	3759.74	2
HD51303	-0.0111	-0.0021	-0.0025	0.0010	0.0009	0.0012	0.0125	4.508	2925.86	1
HD51426	-0.0123	-0.0052	-0.0050	0.0008	0.0009	0.0009	0.0136	3.106	3466.54	1
HD51790	-0.0089	-0.0025	0.0020	0.0007	0.0007	0.0009	0.0117	0.964	4509.61	1
HD52297	-0.0085	-0.0082	-0.0025	0.0006	0.0006	0.0006	0.0134	1.628	4847.80	2
HD51912	-0.0109	-0.0050	0.0022	0.0008	0.0008	0.0008	0.0124	1.564	3051.63	2
HD52567	-0.0451	-0.0046	-0.0012	0.0007	0.0007	0.0011	0.0118	11.947	5083.90	1
HD52669	-0.0155	-0.0017	-0.0002	0.0006	0.0006	0.0010	0.0112	29.470	5084.90	1
HD52589	-0.0100	0.0006	0.0012	0.0007	0.0007	0.0020	0.0110	1.684	1905.69	1
HD52693	-0.0130	-0.0016	0.0011	0.0006	0.0007	0.0010	0.0107	2.446	5162.77	1
HD53021	-0.0139	-0.0105	0.0078	0.0009	0.0009	0.0009	0.0148	3.754	3159.46	2
HD53067	-0.0096	-0.0006	0.0048	0.0011	0.0011	0.0015	0.0159	3.276	2566.80	1
HD53081	-0.0095	-0.0044	0.0037	0.0009	0.0009	0.0010	0.0121	5.873	3087.60	1
HD53204	-0.0109	-0.0010	-0.0004	0.0009	0.0009	0.0016	0.0132	2.285	4181.61	1
HD53695	-0.0098	-0.0034	-0.0094	0.0009	0.0009	0.0008	0.0134	0.839	2202.78	1
HD53851	-0.0133	0.0000	0.0003	0.0008	0.0008	0.0018	0.0112	2.025	2925.86	1
HD54445	-0.0115	-0.0012	-0.0028	0.0007	0.0006	0.0010	0.0119	0.657	5118.83	1
HD54544	-0.0124	-0.0012	0.0010	0.0007	0.0007	0.0012	0.0138	2.229	3812.58	1
HD54766	-0.0173	-0.0025	0.0028	0.0007	0.0008	0.0010	0.0141	1.993	4531.60	1
HD54962	-0.0099	0.0004	0.0071	0.0014	0.0013	0.0018	0.0152	2.542	4837.77	1
HD56273	-0.0150	-0.0075	0.0011	0.0008	0.0008	0.0008	0.0139	1.787	3653.86	2
HD57040	0.0010	0.0068	-0.0011	0.0006	0.0006	0.0007	0.0113	26.952	3034.70	2
HD56748	-0.0168	-0.0002	0.0003	0.0008	0.0008	0.0016	0.0132	5.933	2784.50	1
HD56773	-0.0238	0.0015	-0.0013	0.0008	0.0008	0.0023	0.0125	0.768	3759.74	1
HD57372	-0.0066	-0.0081	0.0004	0.0009	0.0009	0.0009	0.0152	7.888	4973.50	2
HD57526	-0.0301	-0.0084	0.0000	0.0006	0.0006	0.0007	0.0114	3.344	1967.56	2
HD57946	-0.0082	0.0006	0.0000	0.0007	0.0007	0.0022	0.0123	2.158	1874.81	1
HD58378	-0.0154	-0.0003	0.0022	0.0008	0.0009	0.0017	0.0135	1.818	2171.86	1
HD58151	-0.0175	-0.0030	-0.0025	0.0010	0.0010	0.0014	0.0168	2.536	2694.67	1
SAO173716	-0.0197	-0.0035	0.0016	0.0009	0.0009	0.0013	0.0152	2.483	3503.48	1
HD58794	-0.0087	-0.0093	-0.0003	0.0008	0.0009	0.0009	0.0146	2.800	1869.78	2
HD59164	-0.0134	-0.0045	-0.0036	0.0008	0.0008	0.0009	0.0187	4.330	1888.73	1
HD59574	-0.0133	-0.0040	-0.0004	0.0007	0.0007	0.0008	0.0111	1.607	3447.58	1
HD59437	-0.0170	0.0009	-0.0044	0.0010	0.0010	0.0023	0.0137	10.801	4769.80	1
HD59379	-0.0083	-0.0038	0.0013	0.0010	0.0010	0.0010	0.0173	1.025	4526.64	2
HD59758	-0.0111	0.0002	-0.0007	0.0008	0.0008	0.0018	0.0127	2.170	4889.76	1
HD59716	-0.0336	0.0058	0.0043	0.0012	0.0013	0.0076	0.0159	4.333	4133.75	1
HD59752	-0.0221	-0.0015	-0.0003	0.0008	0.0008	0.0013	0.0123	2.667	1963.57	1
HD59982	-0.0001	-0.0072	-0.0071	0.0009	0.0009	0.0009	0.0128	5.129	1933.60	2
HD59981	-0.0236	-0.0045	0.0097	0.0008	0.0008	0.0010	0.0152	1.446	4509.74	1
HD60908	-0.0104	-0.0049	0.0004	0.0006	0.0006	0.0007	0.0116	1.546	2635.67	2
HD61334	-0.0142	-0.0024	0.0034	0.0008	0.0008	0.0011	0.0141	19.150	2559.60	1
HD61134	-0.0062	-0.0067	0.0000	0.0008	0.0008	0.0008	0.0141	4.617	1968.65	2
HD61369	-0.0197	-0.0019	0.0107	0.0011	0.0011	0.0014	0.0147	1.944	4216.55	1
HD61368	-0.0119	-0.0128	-0.0064	0.0006	0.0006	0.0006	0.0119	1.824	2240.81	2
HD61622	-0.0049	-0.0165	-0.0055	0.0007	0.0007	0.0008	0.0137	0.852	2188.84	2
HD61490	-0.0119	-0.0007	0.0101	0.0013	0.0013	0.0014	0.0172	1.315	4741.89	1
HD61731	-0.0073	-0.0022	-0.0029	0.0007	0.0007	0.0008	0.0134	8.652	3411.60	1
CD-443656	-0.0115	0.0040	-0.0058	0.0015	0.0015	0.0038	0.0119	1.061	4521.70	2
HD62244	-0.0205	-0.0051	-0.0006	0.0008	0.0008	0.0009	0.0139	16.300	3769.70	1
HD62446	-0.0175	-0.0034	0.0048	0.0006	0.0006	0.0008	0.0119	31.600	2251.00	1
HD62535	-0.0453	-0.0106	0.0091	0.0007	0.0007	0.0009	0.0113	2.451	4622.49	1
HD63204	-0.0085	-0.0049	-0.0017	0.0006	0.0006	0.0007	0.0129	1.838	1965.58	2
HD62632	-0.0186	-0.0072	0.0012	0.0007	0.0007	0.0008	0.0122	3.280	3048.66	2
HD63728	-0.0245	0.0015	0.0077	0.0012	0.0012	0.0027	0.0166	1.840	4870.64	1
HD63304	-0.0074	-0.0067	0.0013	0.0006	0.0006	0.0006	0.0115	1.313	1919.72	2
HD64369	-0.0054	-0.0161	0.0062	0.0008	0.0008	0.0008	0.0169	0.891	4105.68	2
HD64288	-0.0105	-0.0009	0.0025	0.0008	0.0008	0.0013	0.0139	1.284	3509.58	1
HD64881	-0.0070	0.0001	0.0023	0.0006	0.0006	0.0011	0.0092	1.104	3057.62	1
HD64901	-0.0059	-0.0011	0.0004	0.0006	0.0006	0.0008	0.0098	4.061	2252.76	1
CPD-60944A	-0.0163	-0.0134	-0.0052	0.0007	0.0007	0.0007	0.0121	3.737	2654.70	2
HD65570	-0.0233	-0.0062	0.0009	0.0008	0.0008	0.0010	0.0137	1.770	2191.82	1
HD65743	-0.0087	-0.0004	-0.0025	0.0008	0.0009	0.0014	0.0129	1.844	2944.81	1
HD66821	-0.0092	0.0002	0.0000	0.0007	0.0007	0.0016	0.0127	154.900	2928.00	1
HD66766	-0.0211	-0.0105	0.0029	0.0006	0.0006	0.0006	0.0135	1.607	3858.52	2
HD66991	-0.0123	0.0011	0.0034	0.0008	0.0007	0.0021	0.0099	1.037	4574.59	1
HD67217	-0.0139	0.0004	-0.0126	0.0014	0.0014	0.0016	0.0108	2.438	3516.53	2
HD67868	-0.0155	-0.0009	0.0050	0.0008	0.0008	0.0012	0.0122	2.758	2667.74	1
HD67951	-0.0165	-0.0030	0.0126	0.0010	0.0010	0.0011	0.0130	1.157	4827.73	1
HD67982	-0.0158	-0.0076	-0.0036	0.0005	0.0005	0.0006	0.0091	1.118	4540.75	2
HD68480	-0.0337	-0.0252	0.0148	0.0009	0.0009	0.0009	0.0154	7.333	1950.60	2
HD68476	-0.0079	-0.0044	-0.0029	0.0008	0.0008	0.0008	0.0135	0.840	3055.57	2
CPD-372043	-0.0204	-0.0037	0.0079	0.0013	0.0013	0.0015	0.0196	6.295	3076.60	1
HD69193	-0.0104	-0.0035	-0.0029	0.0008	0.0008	0.0009	0.0136	2.694	3406.80	1
HD69544	-0.0311	-0.0080	-0.0037	0.0006	0.0007	0.0008	0.0121	236.500	2810.00	1
HD69825	-0.0120	-0.0019	-0.0006	0.0008	0.0008	0.0011	0.0139	3.318	1964.60	1
HD69913	-0.0200	-0.0015	-0.0057	0.0008	0.0009	0.0014	0.0135	19.975	1977.60	1
HD69932	-0.0064	-0.0060	-0.0035	0.0005	0.0005	0.0005	0.0109	2.305	3711.84	2
HD70045	0.0153	0.0052	0.0012	0.0006	0.0007	0.0007	0.0112	5.306	1925.70	1
HD70749	-0.0020	-0.0100	0.0033	0.0007	0.0007	0.0008	0.0123	2.358	4091.73	2
HD70817	-0.0119	-0.0032	-0.0015	0.0007	0.0007	0.0008	0.0104	3.509	4181.73	1
HD71860	-0.0094	-0.0108	-0.0145	0.0009	0.0010	0.0008	0.0145	8.634	2900.80	2
HD72140	-0.0036	-0.0061	-0.0071	0.0008	0.0007	0.0007	0.0135	0.540	4530.72	2
HD72055	-0.0125	-0.0015	0.0008	0.0007	0.0007	0.0011	0.0153	2.709	3057.63	1
CD-335120	-0.0036	-0.0144	-0.0033	0.0006	0.0006	0.0007	0.0130	5.683	1889.80	2
HD72801	-0.0238	0.0020	0.0045	0.0009	0.0009	0.0026	0.0168	3.005	4570.71	1
HD73063	-0.0164	-0.0012	-0.0006	0.0006	0.0006	0.0011	0.0140	2.322	2698.72	1
HD73009	-0.0075	-0.0010	-0.0027	0.0005	0.0005	0.0007	0.0111	0.855	3495.55	1
CD-513094	-0.0138	-0.0021	0.0088	0.0008	0.0008	0.0008	0.0115	5.306	1994.60	1
HD73607	-0.0253	0.0004	0.0041	0.0006	0.0006	0.0012	0.0149	2.742	2033.50	1
HD73850	-0.0296	-0.0006	0.0029	0.0007	0.0007	0.0014	0.0120	1.249	2083.45	1
HD73737	-0.0094	-0.0003	-0.0027	0.0008	0.0008	0.0014	0.0144	39.670	1948.70	1
HD74423	-0.0082	-0.0008	0.0018	0.0008	0.0008	0.0012	0.0159	0.790	2606.86	1
SAO220259	-0.0109	-0.0002	-0.0010	0.0008	0.0008	0.0017	0.0147	14.304	3036.60	1
HD74636	-0.0226	0.0014	0.0029	0.0008	0.0008	0.0022	0.0124	0.655	3666.84	1
HD74672	-0.0065	-0.0021	-0.0010	0.0007	0.0007	0.0008	0.0127	4.528	2709.70	1
HD74821	-0.0218	-0.0019	-0.0011	0.0007	0.0007	0.0011	0.0157	2.963	2071.47	1
HD75293	-0.0073	-0.0014	-0.0033	0.0008	0.0007	0.0009	0.0130	1.522	1950.65	1
HD75323	-0.0230	-0.0019	-0.0031	0.0007	0.0007	0.0012	0.0118	12.625	4626.50	1
HD76504	-0.0069	-0.0037	-0.0045	0.0008	0.0009	0.0008	0.0136	0.903	4385.84	2
HD76283	-0.0156	-0.0052	-0.0081	0.0008	0.0007	0.0007	0.0114	1.947	3773.64	1
HD76439	-0.0269	-0.0243	0.0004	0.0013	0.0012	0.0012	0.0214	1.472	4253.58	2
HD76590	-0.0167	-0.0012	-0.0024	0.0010	0.0010	0.0016	0.0150	2.628	3462.66	1
HD76650	-0.0130	-0.0006	0.0045	0.0006	0.0006	0.0010	0.0132	1.983	3016.77	1
BD-212641	-0.0196	0.0013	0.0053	0.0008	0.0008	0.0019	0.0120	2.289	2763.59	1
HD77013	-0.0092	-0.0048	-0.0003	0.0007	0.0007	0.0008	0.0126	0.412	3787.70	2
HD77885	-0.0084	-0.0083	0.0104	0.0005	0.0006	0.0005	0.0120	0.946	3086.64	2
HD77689	-0.0221	0.0009	-0.0037	0.0010	0.0010	0.0024	0.0156	8.596	3850.30	1
HD78201	-0.0153	-0.0018	0.0069	0.0012	0.0012	0.0016	0.0175	1.559	1907.73	1
HD78568	-0.0009	-0.0132	0.0061	0.0004	0.0005	0.0006	0.0125	3.204	1887.71	2
HD78651	-0.0077	0.0027	-0.0034	0.0016	0.0016	0.0047	0.0156	23.916	4881.60	2
HD78942	-0.0060	-0.0004	0.0001	0.0006	0.0006	0.0011	0.0124	24.184	4485.70	1
HD79606	-0.0410	-0.0051	0.0017	0.0006	0.0006	0.0010	0.0142	2.093	2185.75	1
HD79794	-0.0163	-0.0019	-0.0102	0.0009	0.0008	0.0010	0.0146	1.499	3529.60	1
HD79976	-0.0127	-0.0139	-0.0077	0.0006	0.0006	0.0006	0.0121	1.426	3768.78	2
HD80485	-0.0339	-0.0053	-0.0003	0.0005	0.0005	0.0007	0.0092	2.502	1959.63	1
HD81349	-0.0140	-0.0103	-0.0080	0.0008	0.0008	0.0008	0.0136	0.589	4641.50	2
HD81289	-0.0220	-0.0014	0.0015	0.0010	0.0010	0.0018	0.0164	1.858	1977.62	1
HD81877	-0.0114	-0.0014	-0.0061	0.0011	0.0010	0.0013	0.0140	3.215	3175.49	1
HD82154	-0.0119	-0.0045	0.0039	0.0008	0.0007	0.0008	0.0126	4.620	4089.79	1
HD82691	-0.0101	-0.0010	-0.0016	0.0005	0.0005	0.0008	0.0126	19.807	2201.00	1
HD82917	-0.0183	0.0077	-0.0029	0.0009	0.0009	0.0034	0.0136	2.246	3861.60	2
HD83002	-0.0126	0.0006	0.0018	0.0010	0.0010	0.0026	0.0166	1.551	4259.56	1
HD82944	-0.0228	-0.0009	0.0031	0.0008	0.0007	0.0015	0.0124	2.479	4959.59	1
HD83467	-0.0217	-0.0015	-0.0005	0.0008	0.0008	0.0013	0.0132	7.191	1941.60	1
HD84001	-0.0115	0.0003	-0.0039	0.0010	0.0010	0.0020	0.0134	0.541	4231.57	1
HD84448	-0.0226	-0.0043	-0.0052	0.0007	0.0008	0.0009	0.0122	1.013	3061.59	1
HD84690	-0.0119	-0.0009	-0.0005	0.0009	0.0008	0.0015	0.0144	8.121	4152.70	1
HD84656	-0.0068	-0.0067	-0.0052	0.0008	0.0007	0.0007	0.0142	2.469	1979.60	2
HD84642	-0.0086	-0.0096	-0.0064	0.0008	0.0008	0.0008	0.0128	6.405	3759.70	2
HD84865	-0.0107	0.0007	0.0051	0.0013	0.0013	0.0025	0.0139	2.091	3528.54	1
HD85469	-0.0298	-0.0209	-0.0104	0.0007	0.0007	0.0007	0.0137	2.431	3064.60	2
HD85629	-0.0092	0.0006	-0.0010	0.0007	0.0007	0.0020	0.0112	1.720	2752.57	1
HD85453	-0.0140	-0.0045	-0.0058	0.0009	0.0009	0.0010	0.0147	1.714	1934.54	1
HD85767	-0.0226	-0.0021	-0.0026	0.0007	0.0007	0.0011	0.0145	7.279	1945.70	1
HD85873	-0.0276	-0.0105	0.0027	0.0007	0.0007	0.0008	0.0120	3.752	2212.82	2
HD304810	-0.0106	-0.0102	0.0012	0.0007	0.0007	0.0007	0.0151	2.432	4150.81	2
HD86253	-0.0275	-0.0044	-0.0003	0.0008	0.0009	0.0011	0.0149	0.613	1907.78	1
HD87528	-0.0273	-0.0017	0.0010	0.0007	0.0007	0.0013	0.0131	50.350	2212.80	1
HD87881	-0.0140	-0.0006	0.0033	0.0008	0.0008	0.0014	0.0128	1.455	3802.62	1
HD88042	-0.0240	-0.0165	0.0019	0.0007	0.0007	0.0007	0.0127	6.998	2691.70	2
HD88343	-0.0283	-0.0015	-0.0006	0.0010	0.0010	0.0019	0.0136	22.085	4181.80	1
HD88385	-0.0135	-0.0011	0.0038	0.0008	0.0008	0.0013	0.0123	6.510	1919.70	1
HD88485	-0.0121	-0.0016	0.0041	0.0006	0.0006	0.0009	0.0126	8.009	4205.70	1
HD88488	-0.0212	-0.0016	0.0023	0.0007	0.0008	0.0013	0.0128	0.862	3146.55	1
HD88757	-0.0160	-0.0020	-0.0079	0.0012	0.0011	0.0014	0.0158	6.127	4254.60	1
HD89519	-0.0084	-0.0005	0.0030	0.0008	0.0008	0.0013	0.0116	2.610	2811.57	1
HD299070	-0.0147	-0.0011	-0.0041	0.0008	0.0008	0.0012	0.0163	6.339	2707.70	1
HD89726	-0.0069	0.0003	0.0015	0.0008	0.0008	0.0021	0.0120	5.542	2703.70	1
HD90730	-0.0097	-0.0021	-0.0005	0.0008	0.0008	0.0010	0.0131	1.897	4111.82	1
HD307699	-0.0261	-0.0153	-0.0016	0.0009	0.0009	0.0009	0.0160	5.187	4772.80	2
HD91087	-0.0364	0.0013	-0.0011	0.0008	0.0008	0.0022	0.0171	7.709	4926.70	1
HD91735	-0.0360	-0.0226	-0.0004	0.0008	0.0008	0.0008	0.0134	9.775	4629.50	2
HD300860	-0.0085	-0.0013	0.0023	0.0007	0.0008	0.0010	0.0124	2.590	3411.81	1
HD92190	-0.0077	-0.0102	0.0033	0.0006	0.0007	0.0006	0.0124	1.241	4230.64	2
HD92286	-0.0136	-0.0059	0.0030	0.0012	0.0013	0.0013	0.0268	13.916	2697.70	2
HD92379	-0.0088	-0.0014	0.0025	0.0006	0.0006	0.0008	0.0130	1.634	4441.79	1
HD92849	-0.0106	0.0010	-0.0007	0.0006	0.0006	0.0021	0.0133	2.710	2944.84	1
HD305451	-0.0122	-0.0023	-0.0034	0.0007	0.0007	0.0009	0.0135	8.156	3870.70	1
HD93821	-0.0308	-0.0018	-0.0140	0.0007	0.0008	0.0011	0.0162	5.835	1964.30	1
HD94111	-0.0136	-0.0002	-0.0014	0.0007	0.0007	0.0014	0.0113	1.221	3129.73	1
HD94873	-0.0246	-0.0060	-0.0021	0.0007	0.0007	0.0009	0.0122	1.817	2820.60	1
HD95974	-0.0428	-0.0072	0.0000	0.0008	0.0008	0.0011	0.0135	5.516	5010.50	1
HD95987	-0.0130	-0.0019	-0.0015	0.0005	0.0005	0.0007	0.0123	1.527	4974.53	1
HD96910	-0.0238	-0.0010	-0.0009	0.0007	0.0007	0.0015	0.0158	13.383	1965.70	1
HD97655	-0.0104	-0.0114	-0.0003	0.0007	0.0007	0.0007	0.0118	5.371	2030.60	2
HD97986	-0.0057	0.0000	0.0048	0.0014	0.0014	0.0016	0.0132	4.354	1878.79	1
HD98486	-0.0025	-0.0048	-0.0099	0.0012	0.0012	0.0009	0.0139	1.614	4968.55	2
HD99204	-0.0161	-0.0018	-0.0130	0.0011	0.0011	0.0012	0.0130	1.718	3701.84	1
SAO222874	-0.0167	-0.0015	-0.0020	0.0013	0.0013	0.0021	0.0209	4.120	3849.63	1
HD100956	-0.0403	-0.0085	-0.0032	0.0011	0.0011	0.0014	0.0197	2.380	4566.67	1
HD102659	-0.0089	-0.0012	-0.0046	0.0010	0.0010	0.0012	0.0151	2.163	3054.80	1
HD103303	-0.0211	-0.0007	0.0017	0.0014	0.0015	0.0028	0.0228	1.565	3902.49	1
CD-506498	-0.0316	-0.0008	0.0010	0.0007	0.0007	0.0015	0.0116	2.146	3886.67	1
HD103844	-0.0292	-0.0184	0.0015	0.0007	0.0007	0.0007	0.0108	52.950	2234.80	2
HD104044	-0.0365	-0.0109	-0.0035	0.0007	0.0006	0.0008	0.0145	3.049	2635.81	1
HD104314	-0.0205	-0.0088	0.0039	0.0009	0.0009	0.0009	0.0144	4.615	1938.73	2
HD104376	-0.0274	-0.0005	0.0000	0.0005	0.0005	0.0011	0.0126	4.940	3073.80	1
HD105457	-0.0166	0.0018	-0.0022	0.0010	0.0010	0.0034	0.0148	1.738	2234.84	1
HD106688	-0.0084	-0.0046	0.0071	0.0006	0.0006	0.0006	0.0094	2.643	1980.70	2
HD109789	-0.0222	-0.0049	-0.0059	0.0009	0.0008	0.0011	0.0139	2.793	2145.47	1
CPD-731028	-0.0157	-0.0006	-0.0033	0.0007	0.0008	0.0014	0.0136	0.741	2794.53	1
HD111055	-0.0176	-0.0104	-0.0005	0.0006	0.0006	0.0006	0.0130	1.015	2674.83	2
HD112528	-0.0244	-0.0078	0.0016	0.0008	0.0008	0.0009	0.0136	5.783	1963.80	1
HD114696	-0.0351	-0.0099	-0.0005	0.0006	0.0006	0.0008	0.0136	3.562	2071.54	1
HD115789	-0.0284	-0.0085	-0.0051	0.0009	0.0009	0.0010	0.0151	2.121	2083.62	1
HD116864	-0.0283	-0.0095	0.0182	0.0009	0.0009	0.0009	0.0127	2.673	1979.72	1
HD117537	-0.0046	-0.0002	0.0024	0.0009	0.0009	0.0013	0.0130	6.171	2443.50	1
HD117855	-0.0148	-0.0071	-0.0002	0.0007	0.0007	0.0008	0.0111	26.630	3158.70	2
HD118502	-0.0009	-0.0070	0.0069	0.0008	0.0008	0.0008	0.0130	1.824	5002.56	2
HD119343	-0.0137	0.0005	0.0091	0.0013	0.0013	0.0019	0.0119	3.270	3597.53	1
HD119716	-0.0503	-0.0100	-0.0025	0.0021	0.0021	0.0027	0.0349	4.513	3054.80	1
HD121081	-0.0054	-0.0168	-0.0011	0.0008	0.0008	0.0009	0.0156	3.454	2025.61	2
HD123627	-0.0140	0.0024	-0.0030	0.0011	0.0011	0.0049	0.0142	4.392	2173.49	1
HD123927	-0.0110	-0.0104	-0.0151	0.0006	0.0006	0.0006	0.0130	5.780	3981.30	2
TYC8690-1870-1	-0.0316	-0.0093	-0.0032	0.0007	0.0008	0.0009	0.0143	4.918	3836.70	1
HD125903	-0.0238	-0.0080	0.0005	0.0007	0.0007	0.0009	0.0123	1.565	2070.54	2
HD128521	-0.0272	-0.0014	-0.0028	0.0008	0.0008	0.0015	0.0132	4.026	1996.70	1
HD128840	-0.0257	-0.0058	0.0017	0.0008	0.0008	0.0010	0.0134	1.925	2129.47	1
HD129751	-0.0180	-0.0094	0.0069	0.0009	0.0009	0.0009	0.0144	1.390	1966.85	2
HD130336	-0.0217	-0.0055	-0.0036	0.0006	0.0006	0.0007	0.0139	1.295	2725.73	1
HD130423	-0.0114	-0.0057	-0.0049	0.0006	0.0006	0.0007	0.0139	1.211	3168.76	2
HD132988	-0.0188	-0.0010	-0.0047	0.0008	0.0008	0.0014	0.0157	2.564	2548.50	1
HD133246	-0.0136	-0.0010	0.0018	0.0008	0.0008	0.0013	0.0160	1.799	1953.79	1
HD133722	-0.0300	-0.0128	-0.0030	0.0006	0.0006	0.0006	0.0130	2.088	2081.56	2
HD133702	-0.0303	-0.0020	0.0008	0.0005	0.0005	0.0009	0.0114	2.110	2102.49	1
HD134348	-0.0142	-0.0110	0.0025	0.0007	0.0007	0.0006	0.0116	1.225	2791.52	2
HD135800	-0.0298	-0.0024	0.0077	0.0008	0.0008	0.0012	0.0122	6.288	3624.50	1
HD136150	-0.0163	-0.0003	-0.0045	0.0011	0.0011	0.0021	0.0165	2.557	4269.73	1
HD138151	-0.0121	-0.0008	0.0001	0.0011	0.0011	0.0019	0.0212	5.042	1939.80	1
HD138519	-0.0201	-0.0036	0.0019	0.0008	0.0008	0.0011	0.0126	12.340	1936.90	1
HD138773	-0.0159	-0.0107	0.0097	0.0008	0.0008	0.0007	0.0133	3.791	2651.86	2
HD139472	-0.0271	-0.0008	0.0000	0.0011	0.0011	0.0022	0.0184	1.792	2489.51	1
CPD-633687	-0.0137	-0.0098	0.0095	0.0008	0.0008	0.0008	0.0130	0.966	4901.89	2
HD143383	-0.0237	-0.0015	-0.0088	0.0009	0.0009	0.0013	0.0157	5.123	1984.80	1
HD143868	-0.0074	-0.0070	0.0161	0.0010	0.0010	0.0008	0.0172	2.085	1954.82	2
HD144059	-0.0152	-0.0023	0.0023	0.0007	0.0007	0.0010	0.0151	22.213	2094.60	1
CD-546496	-0.0140	-0.0027	-0.0017	0.0010	0.0010	0.0013	0.0164	1.058	1955.83	1
HD144815	-0.0294	-0.0043	0.0044	0.0008	0.0009	0.0012	0.0122	3.410	3112.72	1
HD146269	-0.0316	0.0005	0.0031	0.0008	0.0008	0.0019	0.0146	1.631	2667.86	1
HD146555	-0.0203	0.0086	0.0148	0.0025	0.0025	0.0045	0.0178	1.729	2658.84	2
HD147346	-0.0082	-0.0010	0.0037	0.0009	0.0009	0.0012	0.0147	2.642	1965.78	1
HD147876	-0.0290	-0.0199	-0.0028	0.0008	0.0008	0.0009	0.0142	1.029	2031.72	2
HD148848	-0.0248	0.0007	0.0067	0.0009	0.0009	0.0020	0.0144	8.343	3068.80	1
HD148955	-0.0208	-0.0083	0.0006	0.0008	0.0008	0.0009	0.0150	4.865	1954.80	2
HD149636	-0.0313	-0.0189	-0.0031	0.0007	0.0007	0.0007	0.0144	3.022	3178.59	2
HD149831	-0.0078	-0.0100	-0.0014	0.0009	0.0008	0.0008	0.0153	3.378	2473.51	2
HD149766	-0.0195	0.0000	-0.0058	0.0009	0.0009	0.0018	0.0135	87.300	2461.00	1
HD150529	-0.0438	-0.0088	0.0001	0.0010	0.0010	0.0013	0.0148	28.330	2057.60	1
HD150499	-0.0250	-0.0146	-0.0002	0.0011	0.0011	0.0011	0.0158	2.631	2115.52	2
HD151610	-0.0391	-0.0036	-0.0058	0.0009	0.0009	0.0016	0.0162	2.437	2543.47	1
HD151569	-0.0105	-0.0060	0.0025	0.0009	0.0009	0.0010	0.0149	4.532	1964.81	2
HD152771	-0.0146	-0.0061	-0.0002	0.0007	0.0007	0.0007	0.0119	2.192	1983.90	2
HD153153	-0.0205	-0.0009	0.0146	0.0012	0.0012	0.0014	0.0139	2.192	2703.85	1
HD153192	-0.0144	-0.0011	-0.0022	0.0008	0.0008	0.0013	0.0137	11.357	2102.60	1
HD153218	-0.0111	-0.0042	-0.0023	0.0008	0.0008	0.0008	0.0124	1.902	2086.60	1
HD153735	-0.0317	-0.0129	-0.0108	0.0009	0.0009	0.0010	0.0149	5.725	2739.80	1
HD154645	-0.0139	-0.0080	0.0029	0.0006	0.0006	0.0006	0.0128	2.622	2115.54	2
HD155313	-0.0105	-0.0120	0.0051	0.0010	0.0010	0.0010	0.0150	2.265	1994.77	2
HD157063	-0.0095	-0.0213	0.0017	0.0008	0.0008	0.0008	0.0133	4.728	2158.70	2
HD157644	-0.0112	-0.0020	0.0023	0.0007	0.0007	0.0009	0.0112	4.410	2032.73	1
HD157650	-0.0289	0.0017	0.0053	0.0010	0.0010	0.0025	0.0117	1.348	2104.58	1
HD157678	-0.0122	-0.0041	-0.0064	0.0010	0.0009	0.0009	0.0168	0.908	2008.74	1
HD158336	-0.0172	-0.0035	-0.0002	0.0010	0.0009	0.0013	0.0173	1.760	2131.51	1
HD158160	-0.0036	-0.0151	-0.0056	0.0005	0.0005	0.0006	0.0131	2.283	2008.73	2
HD158596	-0.0198	-0.0005	-0.0035	0.0009	0.0009	0.0015	0.0164	2.022	1953.88	1
HD158919	-0.0155	-0.0122	-0.0047	0.0009	0.0010	0.0010	0.0158	75.720	2705.00	2
HD315873	-0.0197	-0.0003	-0.0019	0.0006	0.0006	0.0012	0.0127	5.277	2129.50	1
HD159898	-0.0258	-0.0011	-0.0075	0.0012	0.0012	0.0019	0.0164	4.797	2085.60	1
HD160731	-0.0103	-0.0006	-0.0007	0.0009	0.0009	0.0017	0.0144	1.465	2787.85	1
HD160711	-0.0062	-0.0133	0.0063	0.0010	0.0010	0.0010	0.0142	1.067	2465.62	2
HD160857	-0.0179	-0.0008	-0.0005	0.0008	0.0008	0.0015	0.0127	6.713	3472.80	1
HD161168	-0.0216	-0.0021	-0.0010	0.0007	0.0007	0.0012	0.0128	1.540	2702.88	1
HD161349	-0.0108	-0.0063	0.0024	0.0008	0.0007	0.0008	0.0138	4.019	2115.57	2
HD161724	-0.0239	0.0006	-0.0088	0.0013	0.0013	0.0025	0.0150	5.688	2040.70	1
HD162108	-0.0096	0.0059	-0.0046	0.0009	0.0008	0.0017	0.0134	0.788	2494.56	2
HD162727	-0.0288	0.0004	-0.0018	0.0012	0.0012	0.0029	0.0173	1.421	3113.81	1
HD164053	-0.0175	-0.0131	0.0006	0.0008	0.0008	0.0008	0.0122	2.951	2117.57	2
HD164560	-0.0419	-0.0175	0.0026	0.0004	0.0003	0.0004	0.0090	10.154	2143.50	2
HD166417	-0.0112	-0.0002	0.0022	0.0012	0.0012	0.0024	0.0119	2.287	2492.76	1
HD166198	-0.0122	-0.0031	-0.0047	0.0008	0.0008	0.0009	0.0117	5.764	2191.50	1
HD168507	-0.0112	-0.0098	0.0011	0.0006	0.0006	0.0006	0.0110	2.847	2145.54	2
HD169005	-0.0121	0.0006	0.0027	0.0009	0.0010	0.0024	0.0128	1.101	4290.70	1
HD172330	-0.0051	-0.0001	0.0007	0.0007	0.0006	0.0014	0.0093	1.275	2117.59	1
HD172703	-0.0276	-0.0013	0.0079	0.0008	0.0008	0.0013	0.0114	19.478	2810.90	1
HD342867	-0.0114	-0.0024	-0.0065	0.0008	0.0008	0.0009	0.0103	5.318	4292.60	1
HD174646	-0.0220	-0.0062	-0.0018	0.0007	0.0008	0.0009	0.0116	1.181	3253.60	1
HD174595	-0.0214	-0.0048	0.0088	0.0009	0.0009	0.0011	0.0136	7.114	2053.70	1
HD175909	-0.0108	-0.0078	-0.0034	0.0007	0.0007	0.0007	0.0110	1.299	2085.68	2
HD177338	-0.0123	-0.0044	-0.0019	0.0008	0.0008	0.0009	0.0140	3.035	2026.77	1
HD177548	0.0082	0.0027	-0.0005	0.0009	0.0009	0.0010	0.0109	0.935	3665.54	2
HD178929	-0.0253	-0.0108	0.0035	0.0012	0.0012	0.0013	0.0153	3.345	2552.50	2
HD180029	-0.0127	-0.0012	-0.0002	0.0010	0.0010	0.0016	0.0140	3.286	2877.60	1
HD180153	-0.0066	-0.0016	-0.0036	0.0009	0.0009	0.0009	0.0111	2.016	2964.51	1
HD180626	-0.0109	-0.0047	0.0002	0.0008	0.0007	0.0008	0.0100	2.289	1998.84	2
HD181550	-0.0158	0.0005	0.0006	0.0010	0.0009	0.0026	0.0116	2.452	2540.64	1
HD182340	-0.0106	0.0018	0.0009	0.0009	0.0009	0.0061	0.0131	2.814	2105.65	1
HD187128	-0.0071	-0.0020	0.0016	0.0009	0.0009	0.0010	0.0129	6.186	2904.60	1
HD189184	-0.0010	-0.0083	0.0076	0.0009	0.0009	0.0009	0.0124	1.179	4722.66	2
HD189963	-0.0087	-0.0042	0.0002	0.0012	0.0012	0.0013	0.0172	10.231	2053.80	2
HD190075	-0.0101	-0.0016	-0.0031	0.0008	0.0008	0.0011	0.0116	1.661	3273.54	1
HD196691	-0.0118	-0.0024	0.0022	0.0010	0.0010	0.0013	0.0139	4.043	2490.65	1
HD206028	-0.0083	-0.0016	0.0003	0.0008	0.0008	0.0011	0.0148	0.786	2813.03	1
HD216116	-0.0085	0.0000	0.0052	0.0017	0.0017	0.0023	0.0142	4.128	2116.70	1
HD2957	-0.0069	-0.0005	0.0028	0.0010	0.0010	0.0015	0.0122	4.633	4627.91	1
HD3885	-0.0074	-0.0026	-0.0013	0.0006	0.0006	0.0007	0.0154	1.815	2910.72	1
HD5823	-0.0092	-0.0026	-0.0014	0.0011	0.0011	0.0013	0.0161	1.245	3765.53	1
HD8783	-0.0059	-0.0008	-0.0036	0.0019	0.0018	0.0022	0.0187	19.396	3794.50	1
HD16145	0.0000	-0.0067	0.0019	0.0007	0.0007	0.0007	0.0111	2.238	4525.52	2
HD20505	-0.0058	-0.0021	0.0035	0.0009	0.0010	0.0010	0.0120	2.044	2666.49	1
HD22032	-0.0089	-0.0003	0.0018	0.0012	0.0012	0.0022	0.0151	4.859	3031.57	1
HD28238	-0.0030	-0.0037	0.0037	0.0007	0.0007	0.0006	0.0104	24.743	2676.50	2
HD30374	-0.0088	-0.0074	-0.0011	0.0007	0.0007	0.0007	0.0110	1.556	3018.65	2
HD240563	-0.0079	-0.0017	0.0048	0.0011	0.0011	0.0012	0.0114	2.945	4399.78	1
HD245155	-0.0090	0.0009	-0.0028	0.0011	0.0012	0.0031	0.0139	0.705	3730.62	1
HD38417	-0.0152	-0.0085	-0.0029	0.0009	0.0009	0.0009	0.0114	2.166	3086.56	2
HD38912	-0.0098	-0.0002	-0.0014	0.0011	0.0011	0.0023	0.0163	1.463	2539.74	1
HD39082	-0.0104	-0.0108	0.0012	0.0008	0.0008	0.0008	0.0139	0.765	4877.58	2
HD40071	-0.0112	-0.0096	-0.0025	0.0012	0.0012	0.0012	0.0173	1.987	4477.82	2
HD40383	-0.0074	-0.0080	0.0019	0.0007	0.0007	0.0007	0.0108	4.036	3644.86	2
HD40678	-0.0060	-0.0003	0.0003	0.0006	0.0006	0.0011	0.0111	22.029	2678.20	1
CD-322739	-0.0088	-0.0126	-0.0027	0.0009	0.0010	0.0009	0.0137	6.993	2910.80	2
HD41869	0.0069	0.0031	0.0007	0.0009	0.0009	0.0010	0.0138	5.235	3655.80	2
HD42574	-0.0052	-0.0007	0.0021	0.0009	0.0009	0.0011	0.0114	0.848	2558.84	1
BD-211382	-0.0063	-0.0019	-0.0025	0.0008	0.0008	0.0010	0.0110	2.295	3819.58	1
HD256476	-0.0064	-0.0010	-0.0006	0.0007	0.0007	0.0010	0.0120	51.230	3106.00	1
HD45029	-0.0056	-0.0023	-0.0062	0.0012	0.0012	0.0010	0.0164	1.909	3480.54	2
HD45698	-0.0072	-0.0030	-0.0014	0.0009	0.0009	0.0010	0.0166	1.085	4350.88	2
HD257776	-0.0081	-0.0006	-0.0036	0.0011	0.0011	0.0016	0.0174	4.922	2886.78	1
HD45582	-0.0061	-0.0001	-0.0022	0.0008	0.0008	0.0015	0.0120	0.678	3068.58	1
HD258428	-0.0094	-0.0029	-0.0037	0.0008	0.0008	0.0009	0.0141	6.878	2922.00	1
HD46105	-0.0027	-0.0051	0.0040	0.0007	0.0007	0.0007	0.0117	0.793	3768.72	2
HD46649	-0.0062	0.0002	-0.0017	0.0010	0.0010	0.0022	0.0159	4.179	3500.80	1
HD48160	-0.0070	-0.0018	-0.0031	0.0012	0.0012	0.0014	0.0161	2.705	4827.71	1
HD48478	-0.0091	-0.0013	-0.0018	0.0009	0.0009	0.0014	0.0129	0.572	2912.88	1
HD49299	-0.0044	-0.0028	0.0020	0.0007	0.0007	0.0007	0.0114	16.172	2762.50	2
HD49797	-0.0058	-0.0017	-0.0001	0.0005	0.0006	0.0007	0.0096	1.226	2201.79	2
BD-141598	-0.0064	-0.0008	-0.0020	0.0008	0.0008	0.0011	0.0126	1.319	2892.91	1
HD50031	-0.0094	0.0005	0.0023	0.0011	0.0011	0.0028	0.0166	2.874	2757.49	1
HD50285	-0.0128	-0.0014	-0.0013	0.0012	0.0013	0.0019	0.0209	0.644	2676.57	1
HD266311	-0.0099	0.0004	0.0011	0.0010	0.0010	0.0025	0.0136	0.947	4521.66	1
HD52264	-0.0098	-0.0012	-0.0078	0.0013	0.0013	0.0014	0.0153	7.823	3731.70	1
HD52599	-0.0069	-0.0038	0.0041	0.0007	0.0007	0.0007	0.0105	9.344	2251.50	2
HD53062	-0.0094	-0.0024	0.0023	0.0009	0.0009	0.0011	0.0144	1.419	3747.80	1
HD54399	-0.0095	-0.0020	-0.0011	0.0010	0.0010	0.0012	0.0157	2.501	3749.73	1
CD-323643	-0.0130	-0.0022	-0.0001	0.0009	0.0009	0.0012	0.0147	0.596	2797.45	1
HD296343	-0.0127	-0.0007	0.0036	0.0011	0.0011	0.0018	0.0165	9.831	5144.70	1
HD53998	-0.0037	-0.0016	-0.0055	0.0010	0.0011	0.0008	0.0127	0.743	4561.51	2
HD56286	-0.0090	-0.0028	0.0026	0.0011	0.0011	0.0012	0.0172	3.397	4849.50	1
HD56366	-0.0106	-0.0006	0.0000	0.0007	0.0007	0.0013	0.0131	5.087	2544.90	1
HD56907	-0.0099	-0.0014	-0.0008	0.0006	0.0006	0.0008	0.0127	8.823	4091.30	1
HD57141	-0.0055	-0.0023	0.0044	0.0011	0.0011	0.0010	0.0161	1.897	4582.58	1
BD-071884	-0.0117	-0.0053	-0.0002	0.0008	0.0008	0.0009	0.0169	75.970	1873.00	2
CD-245203	-0.0065	-0.0023	-0.0084	0.0013	0.0013	0.0009	0.0141	13.215	3758.40	2
HD57368	-0.0088	-0.0020	-0.0022	0.0008	0.0008	0.0011	0.0147	3.529	3445.56	1
HD57683	-0.0058	-0.0044	0.0016	0.0011	0.0010	0.0010	0.0182	2.271	4363.88	2
HD57964A	-0.0092	-0.0115	0.0082	0.0008	0.0008	0.0007	0.0141	0.676	2252.76	2
HD58868	-0.0178	-0.0081	-0.0001	0.0008	0.0008	0.0008	0.0148	2.638	4919.51	2
HD59021	-0.0051	-0.0020	-0.0061	0.0008	0.0008	0.0006	0.0107	2.292	3791.70	2
CD-314653	-0.0289	-0.0007	-0.0067	0.0007	0.0007	0.0013	0.0137	4.493	3877.53	1
BD-162004	-0.0080	-0.0026	-0.0016	0.0008	0.0008	0.0009	0.0157	4.981	4600.52	1
HD60572	-0.0066	-0.0009	0.0001	0.0007	0.0007	0.0011	0.0129	1.949	2140.92	1
CD-304807	-0.0100	-0.0002	-0.0014	0.0009	0.0009	0.0018	0.0141	13.868	4517.90	1
HD62005	-0.0052	-0.0027	0.0027	0.0009	0.0009	0.0008	0.0139	1.487	4531.60	2
HD62080	-0.0043	0.0008	0.0036	0.0040	0.0040	0.0056	0.0118	4.433	4818.85	2
HD62752A	-0.0075	-0.0014	0.0003	0.0008	0.0008	0.0012	0.0141	2.317	2944.80	1
HD62821A	-0.0079	0.0003	-0.0010	0.0007	0.0007	0.0017	0.0114	3.835	4509.77	1
HD62905	-0.0044	-0.0006	0.0004	0.0006	0.0006	0.0008	0.0110	16.836	4508.10	1
HD64698	-0.0081	-0.0100	-0.0047	0.0009	0.0009	0.0008	0.0143	3.023	3090.66	2
HD65208	-0.0050	-0.0012	0.0020	0.0009	0.0009	0.0010	0.0137	1.142	3502.55	1
CPD-64810	-0.0029	-0.0030	-0.0059	0.0008	0.0009	0.0007	0.0118	3.774	4215.72	2
HD67313	-0.0095	-0.0078	-0.0024	0.0007	0.0008	0.0008	0.0129	0.826	2213.91	2
HD67398	-0.0059	-0.0015	0.0040	0.0007	0.0008	0.0008	0.0105	2.011	3385.67	1
HD67909	-0.0100	-0.0158	-0.0129	0.0010	0.0010	0.0009	0.0171	2.414	4755.83	2
HD68013	-0.0085	-0.0025	0.0027	0.0008	0.0009	0.0009	0.0163	1.277	3699.78	1
HD67975	-0.0091	-0.0045	-0.0049	0.0011	0.0011	0.0011	0.0172	2.755	3367.64	2
HD68326A	-0.0101	-0.0023	-0.0014	0.0007	0.0007	0.0008	0.0115	5.148	2196.70	1
HD68322	-0.0074	-0.0013	0.0040	0.0009	0.0010	0.0011	0.0172	1.766	4202.65	1
HD68555	-0.0069	-0.0017	0.0004	0.0008	0.0008	0.0011	0.0145	1.819	4227.57	1
HD68807A	-0.0050	-0.0009	0.0005	0.0006	0.0006	0.0009	0.0126	1.720	3802.62	1
BD-212324	-0.0082	-0.0039	0.0060	0.0015	0.0015	0.0014	0.0243	1.756	2192.75	1
HD68781	-0.0070	-0.0047	-0.0006	0.0006	0.0006	0.0006	0.0109	3.211	2754.58	2
HD69146	-0.0280	-0.0081	0.0014	0.0009	0.0010	0.0011	0.0170	1.049	2676.62	1
HD69067A	-0.0082	0.0029	-0.0007	0.0007	0.0007	0.0042	0.0123	3.668	4551.61	2
HD69204	-0.0086	-0.0023	-0.0001	0.0007	0.0007	0.0009	0.0122	1.659	3851.55	1
HD69862	-0.0086	-0.0032	0.0021	0.0007	0.0007	0.0008	0.0115	0.519	4865.64	1
HD69728	-0.0051	-0.0001	0.0009	0.0005	0.0005	0.0011	0.0117	1.638	4884.72	1
HD70123	-0.0020	-0.0041	-0.0082	0.0013	0.0013	0.0010	0.0167	1.895	4700.92	2
HD70464	-0.0102	-0.0064	-0.0102	0.0008	0.0008	0.0007	0.0123	1.093	1984.52	2
BD-192372	-0.0065	-0.0106	0.0065	0.0008	0.0007	0.0007	0.0121	3.295	1905.75	2
HD70847	-0.0049	-0.0014	0.0059	0.0009	0.0010	0.0008	0.0111	1.034	2520.91	2
HD71034A	-0.0053	-0.0011	-0.0008	0.0007	0.0007	0.0009	0.0116	5.400	4531.70	1
HD72034	-0.0053	-0.0027	-0.0022	0.0007	0.0007	0.0007	0.0137	1.670	4258.51	2
HD72634	-0.0112	-0.0027	0.0047	0.0007	0.0007	0.0009	0.0121	0.931	2963.81	1
HD72401	-0.0094	-0.0015	-0.0011	0.0007	0.0007	0.0009	0.0112	2.492	1939.63	1
HD72976	-0.0069	-0.0022	0.0042	0.0009	0.0009	0.0009	0.0138	3.856	4127.66	1
HD72770	-0.0066	0.0012	-0.0017	0.0012	0.0012	0.0049	0.0102	4.792	3413.74	1
CD-374863	-0.0076	-0.0005	0.0012	0.0008	0.0008	0.0014	0.0150	2.313	2628.80	1
HD73101	-0.0069	0.0007	0.0030	0.0013	0.0012	0.0028	0.0130	0.935	2698.54	1
HD74631	-0.0042	-0.0055	-0.0064	0.0008	0.0008	0.0007	0.0123	1.949	2241.76	2
CD-384858	-0.0066	-0.0044	-0.0035	0.0009	0.0009	0.0009	0.0154	9.646	3407.90	2
HD76164	-0.0067	-0.0013	0.0020	0.0010	0.0010	0.0012	0.0170	5.510	3391.80	1
HD76141	-0.0073	-0.0025	0.0060	0.0010	0.0010	0.0010	0.0143	2.538	4862.78	1
HD76424	-0.0068	-0.0003	-0.0009	0.0006	0.0006	0.0011	0.0133	2.481	2228.77	1
HD76877	-0.0098	-0.0013	0.0018	0.0007	0.0007	0.0010	0.0107	13.491	5138.90	1
HD76759A	-0.0035	-0.0026	-0.0034	0.0008	0.0008	0.0007	0.0118	1.206	4125.64	2
HD77044	-0.0055	-0.0007	-0.0019	0.0008	0.0007	0.0011	0.0119	2.911	2249.77	1
HD77716	-0.0102	-0.0018	0.0014	0.0009	0.0009	0.0013	0.0180	3.501	4641.48	1
HD77809	-0.0072	-0.0031	0.0033	0.0005	0.0005	0.0006	0.0118	2.374	2249.75	1
HD311542	-0.0050	0.0003	-0.0033	0.0015	0.0015	0.0022	0.0131	2.585	3674.81	1
HD78930	-0.0048	-0.0039	0.0067	0.0009	0.0009	0.0007	0.0126	2.522	4629.60	2
HD78611	-0.0093	-0.0018	-0.0040	0.0008	0.0008	0.0009	0.0170	18.805	4091.90	1
HD79986	-0.0047	-0.0013	-0.0001	0.0005	0.0005	0.0006	0.0123	5.155	1994.60	1
HD79795	-0.0061	0.0012	0.0009	0.0011	0.0010	0.0067	0.0147	5.450	3386.70	1
HD299978	-0.0064	-0.0036	-0.0012	0.0006	0.0006	0.0006	0.0140	6.702	2232.80	2
HD84451	-0.0057	-0.0004	-0.0008	0.0007	0.0006	0.0012	0.0151	2.742	4643.49	1
HD84653	-0.0070	-0.0002	0.0014	0.0010	0.0010	0.0019	0.0157	3.258	2926.87	1
HD84945	-0.0104	-0.0006	0.0029	0.0008	0.0008	0.0014	0.0124	9.395	4500.80	1
HD85984	-0.0075	-0.0075	0.0034	0.0010	0.0010	0.0010	0.0159	1.789	4656.47	2
HD86405	-0.0056	-0.0008	0.0014	0.0009	0.0009	0.0013	0.0146	4.032	2649.61	1
HD86290	-0.0088	-0.0056	-0.0019	0.0008	0.0008	0.0008	0.0135	1.013	4089.79	2
HD86824	-0.0064	-0.0013	0.0076	0.0013	0.0013	0.0011	0.0153	2.467	4136.81	2
HD87087	-0.0070	-0.0007	0.0013	0.0008	0.0008	0.0013	0.0135	3.139	4193.73	1
HD88814	-0.0045	-0.0007	0.0021	0.0008	0.0008	0.0010	0.0120	1.592	2680.75	1
HD90233	-0.0042	-0.0001	-0.0007	0.0006	0.0006	0.0012	0.0139	1.633	4606.65	1
HD91134	-0.0042	-0.0028	-0.0002	0.0006	0.0006	0.0006	0.0137	3.901	4149.75	2
CD-396470	-0.0060	-0.0021	0.0014	0.0007	0.0006	0.0008	0.0139	1.943	2067.48	1
HD91520	-0.0044	-0.0005	0.0016	0.0009	0.0008	0.0011	0.0134	1.365	2249.83	1
HD91825A	-0.0036	-0.0039	0.0017	0.0007	0.0007	0.0007	0.0112	2.763	4277.57	2
HD91982	-0.0057	-0.0007	-0.0008	0.0008	0.0008	0.0012	0.0135	2.219	2225.82	1
HD92315	-0.0069	-0.0002	0.0075	0.0014	0.0014	0.0013	0.0130	1.577	3905.64	2
HD93500A	-0.0059	-0.0031	0.0015	0.0006	0.0005	0.0006	0.0144	2.363	2660.82	2
HD94052	-0.0054	-0.0002	0.0008	0.0007	0.0007	0.0012	0.0143	7.647	5024.30	1
HD94681	-0.0100	-0.0019	0.0003	0.0008	0.0008	0.0010	0.0130	3.544	2790.52	1
HD95491	-0.0104	0.0001	-0.0049	0.0014	0.0014	0.0023	0.0185	4.854	2990.83	1
HD96471	-0.0038	-0.0038	-0.0075	0.0012	0.0012	0.0009	0.0138	4.930	3528.63	2
HD98340	-0.0097	-0.0017	0.0032	0.0009	0.0008	0.0011	0.0146	3.147	2829.50	1
HD99147	-0.0185	-0.0050	0.0072	0.0009	0.0009	0.0011	0.0162	1.333	4455.79	1
HD99824	-0.0127	0.0002	-0.0030	0.0010	0.0010	0.0021	0.0142	7.220	3407.70	1
HD99826	-0.0075	0.0004	-0.0015	0.0009	0.0009	0.0022	0.0126	0.810	4203.69	1
HD101037	-0.0050	-0.0006	-0.0004	0.0007	0.0007	0.0011	0.0115	0.977	1926.82	1
HD101891	-0.0105	-0.0009	-0.0001	0.0008	0.0007	0.0013	0.0121	0.895	4192.67	1
HD102454	-0.0049	-0.0048	-0.0038	0.0008	0.0007	0.0008	0.0155	2.079	2014.60	2
HD102820	-0.0048	-0.0014	-0.0055	0.0010	0.0010	0.0008	0.0147	1.748	2675.78	2
HD103210	-0.0078	0.0039	0.0003	0.0010	0.0010	0.0033	0.0169	4.716	4135.82	2
HD103457	-0.0057	-0.0022	-0.0025	0.0007	0.0007	0.0007	0.0136	2.232	3826.76	1
HD103671	-0.0104	-0.0020	0.0011	0.0011	0.0011	0.0015	0.0194	2.365	3820.73	1
HD104899A	-0.0072	-0.0027	-0.0009	0.0007	0.0007	0.0008	0.0124	1.181	1919.86	2
HD106204	-0.0085	-0.0035	0.0100	0.0015	0.0014	0.0011	0.0172	4.357	2724.70	2
HD106244	-0.0101	-0.0007	-0.0001	0.0009	0.0009	0.0017	0.0160	1.148	2482.53	1
HD106982	-0.0157	-0.0055	0.0018	0.0010	0.0009	0.0011	0.0155	2.185	2709.70	1
CPD-691655	-0.0071	-0.0034	0.0110	0.0012	0.0012	0.0009	0.0156	2.282	4180.69	2
HD108087	-0.0064	-0.0014	0.0044	0.0009	0.0009	0.0009	0.0118	7.520	3453.80	1
HD109300	-0.0056	-0.0009	0.0004	0.0006	0.0007	0.0009	0.0111	2.632	3183.58	1
HD109809	-0.0040	-0.0068	0.0011	0.0007	0.0007	0.0007	0.0147	4.818	4468.81	2
HD109830	-0.0237	-0.0004	-0.0020	0.0007	0.0007	0.0014	0.0151	3.454	3047.74	1
HD110072	-0.0065	-0.0038	-0.0097	0.0012	0.0012	0.0009	0.0147	22.225	3810.10	2
HD110274	-0.0137	-0.0112	-0.0043	0.0008	0.0008	0.0008	0.0157	265.100	2765.00	2
CD-651322	-0.0058	-0.0038	0.0004	0.0007	0.0007	0.0007	0.0118	3.286	3775.79	2
HD110568	-0.0064	-0.0011	0.0054	0.0010	0.0010	0.0010	0.0137	9.602	2658.80	1
HD112252	-0.0150	-0.0072	0.0015	0.0007	0.0007	0.0007	0.0120	9.602	3548.10	2
HD113434	-0.0103	0.0013	0.0010	0.0011	0.0010	0.0048	0.0168	0.860	4304.57	1
HD114697	-0.0138	-0.0025	0.0028	0.0008	0.0008	0.0011	0.0133	2.344	4164.78	1
HD114721	-0.0085	-0.0022	0.0010	0.0007	0.0007	0.0009	0.0168	2.334	4273.66	1
HD115398	-0.0057	-0.0023	0.0030	0.0009	0.0009	0.0009	0.0188	0.720	3837.73	1
HD115226	-0.0099	-0.0022	0.0013	0.0008	0.0008	0.0010	0.0136	2.988	4612.58	1
HD115440	-0.0131	-0.0040	0.0015	0.0008	0.0008	0.0009	0.0134	5.442	5088.60	1
HD116124	-0.0067	-0.0007	-0.0015	0.0009	0.0009	0.0013	0.0150	2.256	3115.66	1
HD116557	-0.0067	-0.0029	-0.0047	0.0009	0.0009	0.0008	0.0133	0.926	2027.56	1
HD117055	-0.0091	-0.0132	0.0019	0.0008	0.0008	0.0008	0.0145	1.826	3604.50	2
HD117096	-0.0038	-0.0053	-0.0045	0.0009	0.0010	0.0009	0.0145	2.124	4464.83	2
HD117692	-0.0145	-0.0005	0.0039	0.0008	0.0008	0.0014	0.0175	3.280	3074.73	1
HD118167	-0.0083	-0.0007	0.0006	0.0007	0.0007	0.0013	0.0134	0.911	3858.61	1
HD118470	-0.0073	0.0034	-0.0028	0.0012	0.0012	0.0029	0.0148	3.973	3793.86	2
HD118737	-0.0139	-0.0008	0.0029	0.0007	0.0007	0.0012	0.0106	1.778	2853.52	1
HD119238	-0.0132	-0.0024	-0.0004	0.0009	0.0009	0.0013	0.0153	1.741	2676.56	1
HD119474	-0.0047	-0.0209	0.0100	0.0009	0.0009	0.0009	0.0146	1.891	3171.71	2
HD120016	-0.0055	-0.0003	0.0007	0.0006	0.0006	0.0011	0.0121	2.368	3125.67	1
HD121142	-0.0050	-0.0020	0.0009	0.0008	0.0008	0.0009	0.0127	1.691	3497.73	1
HD121265	-0.0173	-0.0005	-0.0023	0.0009	0.0009	0.0019	0.0168	0.783	3421.84	1
HD121675	-0.0049	0.0001	0.0018	0.0010	0.0010	0.0019	0.0137	3.079	4533.60	1
HD121661	-0.0160	-0.0024	-0.0060	0.0010	0.0010	0.0013	0.0147	46.860	4253.60	1
HD121841	-0.0092	-0.0012	0.0007	0.0007	0.0007	0.0010	0.0134	1.085	3753.87	1
HD122463	-0.0038	-0.0032	0.0002	0.0006	0.0006	0.0006	0.0122	1.847	3829.72	2
HD122525	-0.0112	-0.0023	-0.0020	0.0008	0.0008	0.0010	0.0139	26.072	4642.00	1
HD123164	-0.0156	0.0003	0.0056	0.0013	0.0014	0.0025	0.0185	2.520	5042.51	1
HD123350	-0.0143	0.0047	0.0030	0.0036	0.0036	0.0042	0.0142	5.993	5088.50	2
HD124455	-0.0110	-0.0002	0.0067	0.0010	0.0010	0.0014	0.0115	0.606	4338.53	1
HD124598	-0.0060	-0.0038	0.0019	0.0008	0.0008	0.0007	0.0129	2.198	2058.52	2
HD124269	-0.0138	-0.0028	-0.0027	0.0007	0.0007	0.0009	0.0154	3.543	2830.57	1
HD124437	-0.0084	0.0006	-0.0005	0.0006	0.0006	0.0019	0.0126	5.956	4612.40	1
HD125532	-0.0072	-0.0007	0.0083	0.0013	0.0014	0.0011	0.0152	1.812	1961.83	2
HD126322	-0.0066	-0.0018	-0.0001	0.0007	0.0008	0.0009	0.0129	2.867	2878.56	1
HD126786	-0.0097	-0.0002	-0.0065	0.0013	0.0013	0.0017	0.0137	0.854	2826.61	1
HD126876	-0.0063	-0.0041	-0.0015	0.0007	0.0007	0.0007	0.0128	11.426	3804.80	2
HD127021	-0.0168	-0.0048	-0.0114	0.0008	0.0008	0.0008	0.0150	2.014	4514.87	1
HD127224	-0.0075	-0.0148	-0.0098	0.0008	0.0008	0.0008	0.0189	6.503	4669.50	2
HD127957	-0.0091	-0.0004	-0.0012	0.0007	0.0007	0.0012	0.0153	3.280	3798.82	1
HD128226	-0.0098	-0.0023	0.0017	0.0008	0.0008	0.0010	0.0170	2.486	4715.58	1
HD128676	-0.0025	-0.0048	-0.0049	0.0006	0.0006	0.0006	0.0121	2.401	5063.52	2
HD128574	-0.0067	0.0001	0.0019	0.0008	0.0009	0.0017	0.0159	2.137	2476.49	1
HD128997A	-0.0073	0.0010	-0.0021	0.0011	0.0011	0.0036	0.0111	6.738	2456.50	1
HD129460	-0.0111	-0.0009	0.0063	0.0008	0.0008	0.0011	0.0109	1.764	4974.84	1
HD129934	-0.0101	-0.0053	-0.0132	0.0008	0.0008	0.0006	0.0139	2.176	4703.62	2
HD129994	-0.0090	0.0000	0.0025	0.0008	0.0008	0.0015	0.0118	1.510	4698.72	1
HD130382	-0.0061	-0.0028	-0.0003	0.0006	0.0006	0.0007	0.0099	1.669	3444.80	2
HD130660	-0.0004	-0.0158	-0.0028	0.0005	0.0005	0.0006	0.0130	0.718	2755.67	2
HD129899	-0.0072	0.0004	0.0009	0.0008	0.0008	0.0023	0.0130	1.035	4622.77	1
HD131171	-0.0061	-0.0002	0.0007	0.0008	0.0008	0.0015	0.0133	23.452	2722.00	1
HD131505A	-0.0065	0.0003	0.0009	0.0006	0.0006	0.0016	0.0132	1.258	1985.78	1
HD132634	-0.0034	-0.0038	-0.0055	0.0009	0.0009	0.0007	0.0120	1.722	3896.73	2
HD133281	-0.0093	-0.0043	0.0011	0.0008	0.0008	0.0009	0.0136	0.584	4597.68	2
HD133757	-0.0094	-0.0010	0.0022	0.0008	0.0007	0.0012	0.0123	2.433	3454.92	1
HD133428	-0.0018	-0.0004	-0.0020	0.0013	0.0013	0.0011	0.0144	1.518	5037.54	1
HD134465	-0.0094	-0.0024	-0.0001	0.0007	0.0007	0.0009	0.0149	9.221	3492.70	1
HD134507	-0.0042	-0.0008	0.0020	0.0006	0.0007	0.0008	0.0136	1.488	2052.63	1
HD134109	-0.0101	0.0001	0.0025	0.0007	0.0007	0.0013	0.0131	3.758	4701.63	1
HD135815	-0.0049	-0.0020	0.0012	0.0008	0.0008	0.0009	0.0140	14.843	3606.50	1
HD135916	-0.0105	-0.0031	-0.0019	0.0007	0.0007	0.0009	0.0138	1.694	4707.58	1
HD135480	-0.0059	-0.0028	0.0001	0.0007	0.0007	0.0007	0.0111	3.476	4152.92	2
HD136357	-0.0079	-0.0041	0.0008	0.0008	0.0008	0.0009	0.0149	1.925	2676.60	2
HD136467	-0.0042	-0.0070	-0.0082	0.0010	0.0010	0.0009	0.0208	3.822	4654.57	2
HD136024	-0.0039	-0.0017	0.0028	0.0006	0.0006	0.0006	0.0121	3.265	4204.43	1
HD137065	-0.0047	-0.0113	-0.0043	0.0006	0.0006	0.0007	0.0131	6.024	2821.50	2
HD137309	-0.0147	-0.0129	-0.0005	0.0015	0.0015	0.0015	0.0260	2.192	3530.86	2
HD137363	-0.0063	-0.0024	-0.0002	0.0009	0.0008	0.0009	0.0138	19.785	3530.80	2
HD137848	-0.0064	-0.0047	-0.0007	0.0006	0.0006	0.0006	0.0125	3.522	3847.75	2
HD136575	-0.0071	-0.0010	0.0044	0.0015	0.0015	0.0018	0.0199	4.558	2566.53	1
HD138079	-0.0112	0.0008	-0.0025	0.0016	0.0015	0.0041	0.0213	1.675	4962.66	1
HD138167	-0.0053	-0.0039	-0.0074	0.0009	0.0009	0.0007	0.0123	4.708	4298.55	2
HD138209	-0.0054	-0.0008	0.0009	0.0008	0.0009	0.0011	0.0136	1.506	2083.59	1
HD138586	-0.0108	-0.0001	0.0028	0.0011	0.0011	0.0021	0.0158	2.088	3530.87	1
HD139149	-0.0127	-0.0011	0.0027	0.0011	0.0011	0.0018	0.0151	1.645	5093.45	1
HD139631	-0.0063	-0.0012	0.0018	0.0007	0.0007	0.0009	0.0111	2.143	3517.72	1
HD139855	-0.0063	0.0001	0.0007	0.0007	0.0008	0.0017	0.0134	7.238	3808.80	1
HD140532	-0.0089	-0.0035	-0.0012	0.0007	0.0007	0.0008	0.0130	1.071	4644.63	2
HD141317	-0.0107	0.0000	-0.0034	0.0009	0.0009	0.0016	0.0109	5.356	4126.90	1
HD141586	-0.0074	-0.0007	0.0021	0.0008	0.0008	0.0012	0.0125	3.434	2794.58	1
HD141981	-0.0206	0.0012	-0.0018	0.0008	0.0008	0.0022	0.0159	9.047	3906.70	1
HD142554	-0.0083	-0.0016	-0.0032	0.0007	0.0007	0.0009	0.0114	4.265	1931.86	1
HD142823	-0.0057	0.0004	0.0013	0.0009	0.0009	0.0026	0.0170	1.299	2069.61	1
HD142960	-0.0070	-0.0022	-0.0017	0.0009	0.0009	0.0010	0.0198	7.595	2787.80	1
HD144102	-0.0094	-0.0037	-0.0051	0.0010	0.0009	0.0010	0.0143	4.680	4204.81	1
HD144748	-0.0056	0.0009	-0.0003	0.0007	0.0007	0.0048	0.0114	4.955	3037.88	1
HD144264A	-0.0291	0.0004	0.0026	0.0009	0.0009	0.0022	0.0160	1.251	5098.51	1
HD144991	-0.0062	0.0008	0.0003	0.0007	0.0007	0.0034	0.0160	7.253	2512.50	1
HD145364	-0.0104	-0.0013	0.0015	0.0012	0.0012	0.0018	0.0225	3.309	2719.89	1
HD146246	-0.0080	-0.0027	-0.0015	0.0010	0.0010	0.0012	0.0154	1.647	3619.51	1
HD146447	-0.0075	-0.0014	-0.0006	0.0009	0.0009	0.0012	0.0130	2.112	4759.57	1
HD147259	-0.0085	0.0011	0.0050	0.0020	0.0019	0.0036	0.0129	1.929	2750.81	1
HD147345	-0.0071	0.0006	0.0090	0.0010	0.0010	0.0034	0.0156	23.342	2040.70	2
HD328193	-0.0188	-0.0009	0.0028	0.0009	0.0009	0.0016	0.0149	1.806	2853.53	1
CD-641049	-0.0055	-0.0033	0.0000	0.0008	0.0008	0.0008	0.0132	0.542	4651.67	2
CD-2812149	-0.0121	-0.0044	0.0071	0.0010	0.0009	0.0009	0.0123	1.359	3882.76	1
HD148935	-0.0167	-0.0013	-0.0003	0.0008	0.0008	0.0014	0.0137	0.863	3074.90	1
HD149228	-0.0140	-0.0005	0.0075	0.0013	0.0013	0.0018	0.0159	1.540	3558.72	1
HD149115	-0.0067	-0.0059	-0.0091	0.0009	0.0010	0.0008	0.0142	5.939	3866.70	2
HD149236	-0.0110	0.0003	-0.0030	0.0009	0.0009	0.0019	0.0155	3.859	3653.46	1
HD149409	-0.0056	-0.0015	-0.0029	0.0008	0.0008	0.0010	0.0127	3.275	2885.61	1
HD149769	-0.0136	0.0011	0.0020	0.0013	0.0013	0.0038	0.0172	8.242	4130.00	1
HD150323	-0.0128	-0.0085	0.0009	0.0009	0.0009	0.0009	0.0145	5.378	3526.80	2
HD150137	-0.0265	-0.0043	0.0003	0.0008	0.0008	0.0011	0.0129	5.151	4181.90	1
CD-596262	-0.0107	-0.0054	0.0029	0.0008	0.0008	0.0008	0.0112	0.845	2503.58	2
CD-606444	-0.0051	-0.0012	-0.0006	0.0007	0.0007	0.0009	0.0159	4.467	3583.73	1
HD152099	-0.0069	-0.0016	-0.0009	0.0008	0.0008	0.0010	0.0177	3.207	4276.45	1
HD152137	-0.0050	-0.0015	-0.0015	0.0009	0.0009	0.0010	0.0138	1.330	4756.51	1
HD152834	-0.0064	-0.0039	0.0029	0.0008	0.0008	0.0008	0.0129	4.293	3602.32	2
HD153997A	-0.0091	-0.0024	-0.0001	0.0008	0.0008	0.0010	0.0116	5.500	4571.90	1
HD154772	-0.0080	-0.0033	-0.0031	0.0007	0.0007	0.0008	0.0123	7.543	4758.50	1
HD155127	-0.0047	-0.0013	-0.0029	0.0009	0.0009	0.0010	0.0130	5.524	4233.80	1
HD155188	-0.0108	-0.0015	0.0059	0.0010	0.0011	0.0013	0.0139	3.333	2524.55	1
HD155171	-0.0069	-0.0013	0.0002	0.0008	0.0008	0.0011	0.0138	11.464	2730.10	1
HD155366	-0.0085	-0.0060	-0.0022	0.0009	0.0009	0.0009	0.0143	1.859	3790.85	2
HD156495	-0.0118	-0.0010	0.0015	0.0007	0.0007	0.0012	0.0123	1.379	3524.76	1
HD156853	-0.0075	-0.0014	0.0028	0.0010	0.0010	0.0012	0.0150	1.159	4358.55	1
HD156869	-0.0112	-0.0020	-0.0014	0.0008	0.0008	0.0011	0.0137	2.885	2502.50	1
HD158450	-0.0046	-0.0006	0.0026	0.0009	0.0010	0.0011	0.0127	8.524	1997.90	1
HD158202	-0.0077	-0.0006	0.0002	0.0009	0.0009	0.0015	0.0133	6.254	2737.60	1
HD158343	-0.0108	0.0000	-0.0031	0.0008	0.0008	0.0015	0.0139	0.669	2203.51	1
HD158293	-0.0114	-0.0086	0.0012	0.0007	0.0007	0.0008	0.0144	10.445	1986.20	2
HD159379	-0.0114	-0.0017	0.0011	0.0009	0.0010	0.0014	0.0140	8.239	4228.80	1
HD159317	-0.0059	-0.0001	-0.0039	0.0014	0.0014	0.0019	0.0135	2.721	2473.72	1
HD160445	-0.0128	0.0017	-0.0145	0.0042	0.0042	0.0042	0.0156	1.435	4551.83	2
HD159992	-0.0244	-0.0030	0.0005	0.0007	0.0007	0.0010	0.0146	1.558	2452.68	1
HD162651	-0.0078	0.0010	-0.0024	0.0015	0.0015	0.0045	0.0136	0.760	1962.90	1
HD162316	-0.0046	-0.0027	-0.0049	0.0010	0.0010	0.0008	0.0120	9.304	4658.80	2
HD164085	-0.0309	-0.0040	-0.0022	0.0006	0.0006	0.0010	0.0126	1.221	3167.69	1
HD163833	-0.0064	-0.0015	-0.0006	0.0007	0.0007	0.0009	0.0121	12.379	2125.60	1
HD163926	-0.0111	-0.0014	-0.0022	0.0006	0.0006	0.0008	0.0110	1.502	3603.66	1
HD164069	-0.0057	-0.0001	-0.0027	0.0008	0.0008	0.0013	0.0121	1.472	3191.73	1
HD164319	-0.0153	-0.0009	0.0051	0.0011	0.0011	0.0018	0.0160	2.409	2494.62	1
HD164521	-0.0066	-0.0039	0.0003	0.0005	0.0005	0.0006	0.0105	1.482	5021.82	2
HD166016	-0.0110	-0.0005	-0.0013	0.0008	0.0008	0.0015	0.0143	2.654	4905.90	1
HD165772	-0.0097	-0.0078	-0.0015	0.0007	0.0007	0.0007	0.0141	2.091	3581.51	2
HD165972	-0.0105	-0.0008	-0.0026	0.0007	0.0007	0.0011	0.0101	2.760	3541.80	1
HD166804	-0.0087	-0.0021	-0.0009	0.0008	0.0008	0.0010	0.0134	3.704	2482.55	1
HD166921	-0.0075	-0.0018	0.0028	0.0006	0.0006	0.0007	0.0123	0.533	4286.72	1
HD166771	-0.0073	-0.0019	-0.0026	0.0009	0.0009	0.0011	0.0150	5.688	3472.70	1
HD167288	-0.0088	-0.0014	-0.0021	0.0011	0.0011	0.0016	0.0144	4.348	3177.59	1
HD167211	-0.0101	-0.0016	0.0055	0.0005	0.0006	0.0007	0.0129	0.816	4633.76	1
HD167476	-0.0124	-0.0088	0.0042	0.0004	0.0005	0.0004	0.0121	3.290	4298.74	2
HD167592	-0.0058	-0.0002	-0.0005	0.0009	0.0009	0.0017	0.0130	1.709	5085.59	1
HD166953	-0.0061	-0.0019	0.0013	0.0009	0.0009	0.0011	0.0118	2.590	1997.72	1
HD168057A	-0.0163	-0.0073	0.0004	0.0005	0.0004	0.0005	0.0122	13.308	3649.00	2
HD169380	-0.0072	-0.0035	-0.0050	0.0010	0.0010	0.0010	0.0134	4.087	3504.97	1
HD170054	-0.0022	-0.0080	0.0019	0.0008	0.0008	0.0008	0.0114	0.973	3672.50	2
HD169789	-0.0130	-0.0066	-0.0048	0.0006	0.0006	0.0006	0.0097	5.232	3634.50	2
HD170924	-0.0087	-0.0014	-0.0001	0.0006	0.0006	0.0009	0.0135	6.127	2792.60	1
HD171708	-0.0028	-0.0019	-0.0024	0.0006	0.0006	0.0005	0.0109	3.488	2544.49	2
HD172271	-0.0109	-0.0167	0.0051	0.0006	0.0006	0.0006	0.0140	11.534	3175.10	2
HD172319	-0.0232	-0.0029	-0.0038	0.0008	0.0009	0.0012	0.0146	2.412	3455.77	1
HD172480	-0.0056	-0.0021	0.0030	0.0007	0.0007	0.0007	0.0119	0.871	4729.55	1
HD173612	-0.0217	0.0003	0.0084	0.0007	0.0007	0.0012	0.0153	0.778	4546.86	1
HD173657	-0.0105	-0.0016	-0.0001	0.0009	0.0009	0.0013	0.0142	1.938	4969.77	1
HD173361	-0.0060	-0.0017	-0.0024	0.0008	0.0008	0.0009	0.0130	0.832	2698.92	1
HD173562	-0.0048	-0.0035	0.0048	0.0012	0.0012	0.0011	0.0158	2.304	4188.90	2
HD172164	-0.0081	-0.0014	-0.0027	0.0008	0.0008	0.0011	0.0145	1.607	4363.65	1
HD174146	-0.0167	-0.0053	0.0046	0.0008	0.0009	0.0010	0.0114	11.185	3618.00	1
HD174356	-0.0065	-0.0020	0.0003	0.0010	0.0010	0.0011	0.0118	4.043	4765.67	1
HD174598	-0.0103	0.0006	-0.0024	0.0016	0.0015	0.0039	0.0142	0.917	2788.82	1
HD175110	-0.0133	0.0000	-0.0068	0.0013	0.0013	0.0020	0.0134	0.721	2734.86	1
HD176332	-0.0100	-0.0042	-0.0009	0.0007	0.0007	0.0008	0.0127	11.865	4383.80	2
HD176656	-0.0128	-0.0029	0.0031	0.0011	0.0011	0.0014	0.0110	1.043	2061.75	1
HD176519	-0.0099	-0.0025	-0.0002	0.0012	0.0012	0.0015	0.0146	2.085	2521.67	1
HD179711	-0.0137	-0.0035	0.0010	0.0009	0.0008	0.0010	0.0106	2.951	2916.52	1
HD231041	-0.0104	-0.0004	-0.0017	0.0009	0.0009	0.0017	0.0111	10.772	3639.50	1
HD338226	-0.0084	-0.0014	0.0002	0.0011	0.0010	0.0014	0.0123	0.830	2876.56	1
HD231382	-0.0066	-0.0012	-0.0044	0.0011	0.0010	0.0012	0.0100	4.477	4684.69	1
HD183735	-0.0112	-0.0011	-0.0010	0.0012	0.0012	0.0020	0.0138	2.230	3164.72	1
HD184539	-0.0062	-0.0005	-0.0020	0.0009	0.0009	0.0013	0.0115	2.572	4607.77	1
HD353530	-0.0032	-0.0007	0.0007	0.0009	0.0008	0.0011	0.0154	2.087	2737.91	1

Equations

$$F$$

$$\varphi =\phi -{\phi }_0;\phi =\mathrm{frac}\left(\frac{t-M_0}{P}\right).$$

$${\int }_0^1{F}_1^2(\varphi )\mathrm{d}\varphi$$

$${\int }_0^1{F}_2^2(\varphi )\mathrm{d}\varphi$$

$${\int }_0^1{F}_3^2(\varphi )\mathrm{d}\varphi$$

Full text

*Aims. *The present study aims at detecting underlying patterns in the distribution of photometric spots in a sample of 650 magnetic, chemically peculiar stars and examines their link to the magnetic field topology.

*Methods. *Photometric time-series observations from the ASAS-3 archive were employed to inspect the light-curve morphology of our sample stars and divide them into representative classes described using a principal component analysis. Theoretical light curves were derived from numerous simulations assuming different spot parameters and following the symmetry of a simple dipole magnetic field. These were subsequently compared with the observed light curves.

*Results. *The results from our simulations are in contradiction with the observations and predict a much higher percentage of double-wave light curves than is actually observed. We thereby conclude that the distribution of the chemical spots does not follow the magnetic field topology, which indicates that the role of the magnetic field in the creation and maintenance of the surface structures may be more subsidiary than what is predicted by theoretical studies.

1 Introduction

Chemically peculiar (CP) stars are members of the upper part of the main sequence (spectral types B to F). They are generally slow rotators and are characterized by spectral peculiarities that indicate unusual atmospheric abundances of some chemical elements. This is due to the effects of radiative diffusion and gravitational settling (LeBlanc et al. 2009; Alecian & Stift 2010; Alecian 2015), which result in some elements being lifted to the outer parts of the stellar atmosphere while others settle down into the lower parts.

Some groups of CP stars (the so-called Ap/CP2 stars and the He-weak/CP4 stars; cf. Preston 1974) exhibit global magnetic fields with strengths up to several tens of kilogauss (Aurière et al. 2007) and are characterized by surface abundance inhomogeneities (‘chemical spots’).111For convenience, these stars are referred to hereafter as magnetic, chemically peculiar (mCP) stars. Flux is redistributed in these spots (e.g., Peterson 1970; Molnar 1973; Krtička et al. 2013) and, as the star rotates, the changing viewing angle results in periodic spectroscopic and photometric variations. Stars exhibiting this kind of rotational variability are traditionally referred to as $\alpha^{2}$ Canum Venaticorum (ACV) variables.

While a precise understanding of the processes involved in the formation of the surface structures is still missing (Krtička et al. 2013), it is believed that the magnetic field plays a decisive role (LeBlanc et al. 2009; Alecian & Stift 2010; Alecian 2015). The present study aims at detecting underlying patterns in the distribution of photometric spots and examines their link to the magnetic field topology.

2 Analysis of observations

2.1 Data characteristics

The original data for our research were gleaned from the third phase of the All Sky Automated Survey (ASAS) project, which focused on continuous photometric coverage of the southern sky and part of the northern sky with the goal of detecting any kind of photometric variability. During the third phase of the project (ASAS-3), observations were acquired in Johnson V (Pojmanski et al. 2005). In total, 11 509 variable stars brighter than $V=15$ mag were cataloged by the ASAS team, of which 7 310 remained unclassified. Bernhard et al. (2015) used ASAS-3 data to search for new photometric variables among known mCP stars from the catalogue of Renson & Manfroid (2009) and identified 316 stars with photometric characteristics of ACV variables. Using refined search criteria, Hümmerich et al. (2016) subsequently discovered another 334 ACV variables in these data.

As basis for the present investigation, we employed the original ASAS-3 data of the 650 ACV variables identified by Bernhard et al. (2015) and Hümmerich et al. (2016). We also used their ephemerides, such as the period and Julian date of photometric maximum. ASAS-3 data contain information about Julian Date, brightness using different photometric apertures, corresponding errors, and quality of measurements. We used measurements from the aperture with the lowest errors for a specific star following the methodology of Pojmanski et al. (2005). For the brightest stars ($V<9$ mag), the largest aperture (6 pixels in diameter) was employed; for faint stars ($V>12$ mag), we used the smallest aperture (2 pixels in diameter). Furthermore, lower-quality measurements (indicated by flags ‘C’ and ‘D’; for details see Pojmanski et al. 2005) were excluded from the analysis.

2.2 Principal component analysis of the light curves

According to the shape of the light curves of the mCP stars studied by Bernhard et al. (2015) and Hümmerich et al. (2016), we can divide them into simple categories: single-wave, double-wave, and symmetric or asymmetric light curves. To confirm and mathematically describe these classes, we used a principal component analysis (PCA). This method transforms the original data into a system with new coordinates, which are chosen such that they follow the most common patterns in the data. This coordinate system is based on the combination of the eigenvectors with large eigenvalues. Therefore, we can create principal components and use them to describe the light curve data as their linear combinations. For a detailed description of the modifications of PCA, we refer to Mikulášek (2007).

As PCA requires common data points for all light curves (phase points in this case), we divided all measurements for any given star into 25 phase bins. Every phase bin of each star is then represented by its average value of intensity in the $V$ filter. Applying PCA, we acquired full sets of principal components. These components were fitted by harmonic polynomials of second order, and fit parameters and their errors were obtained. We discovered that only the first five components are meaningful, as their fitted parameters have higher values than their errors multiplied by three. The eigenvalues of these components are 1.89, 0.17, 0.16, 0.03, and 0.03. For simplicity we decided to work only with the first three principal components. These are shown in Fig. 1.

The first component represents a typical mCP-star light curve, which is a symmetric single wave with a relatively sharp maximum and very flat minimum. This light-curve profile can be simulated by assuming one bright photometric spot centered at phase zero. The second principal component is a symmetric double-wave light curve with uneven minima. The third component represents an antisymmetric light curve with the inflection points at phases 0.0 and 0.5, expressing the antisymmetry of light curves. These three components are sufficient to adequately describe all light curves, as indicated by Fig. 2, which illustrates the binned light curves of the first ten stars of our sample overlaid with the smoothed data obtained as a linear combination of the first three principal components.

2.3 Phenomenological model

As has been pointed out, PCA shows that the model function can be satisfactorily described by only the first three principal components, with the first two components being symmetrical and the third one antisymmetrical with regard to phase zero. All of the components can be well approximated by a harmonic polynomial of the second order (see also Mikulášek et al. 2007b; Bernhard et al. 2015). This allows us to express the ASAS-3 mCP-star light curves in a simple form with sufficient accuracy (which is quantitatively evaluated in Fig. 3), using only three free parameters describing their shape:

[TABLE]

where

[TABLE]

Here, $F$ represents the apparent magnitude in the $V$ filter and $\varphi$ is the phase. We used the period values ($P$) and times of maximum ($M_{0}$) derived by Bernhard et al. (2015) and Hümmerich et al. (2016). Calculations were complicated by the fact that, employing this model function, we need to work with a nonlinear regression. However, we can assume that the nonlinear parameter $\varphi_{0}$ has a value near zero, as the light curves have their photometric maxima centered at phase zero, defined by the parameter $M_{0}$.

In this model, the parameters $A_{1}$, $A_{2}$, and $A_{3}$ represent, respectively, the semi-amplitudes of the single-wave, the double-wave, and the antisymmetric terms of the light curve. The special form of the antisymmetric part results from two factors: (a) the first derivative in zero phase has to be zero to ensure the position of the maximum; (b) the value of parameter $A_{3}$ is modified by the coefficient $2/\sqrt{5}$, which normalizes it to the other two parameters. The normalization has been derived from integration of partial function squares:

[TABLE]

As the parameters $A_{1}$, $A_{2}$, and $A_{3}$ are normalized, we can introduce an effective semi-amplitude $A$, where $A=\sqrt{A_{1}^{2}+A_{2}^{2}+A_{3}^{2}}$ , in agreement with a general definition of the quantity in Mikulášek et al. (2007a).

With the prepared model functions described by Eq. 1, we were able to fit the original data in unbinned form and derive values of the parameters $F_{0}$, $A_{1}$, $A_{2}$, and $A_{3}$ for all analyzed stars, which are given in the Appendix (Section A).

2.4 Peculiarities of ASAS-3 data

ASAS-3 data suffer from occasional inhomogeneities, which cause shifts in the mean brightness level of the observations (see e.g., the case of HD 151610 depicted in Fig. 4). This problem can be solved if different values of the parameter $F_{0}$ in Eq. 1 are assumed for the different data sets $(F_{0i})$. However, this procedure has to be performed after the elimination of outliers, which we identified using a 3.5 $\sigma$ interval. In addition, data sets with less than four measurements need to be removed because they contain less points than the number of free parameters. Our analysis showed that, in some extreme and rare cases, the zero-point shifts between different data sets amount to about 0.05 mag.

The described phenomenological model enables us to fit the ASAS-3 data with high accuracy using at least four parameters, which depends on the number of parameters $F_{0i}$. The standard deviations of the fit increase from 0.01 mag for stars of the seventh magnitude to approximately 0.03 mag for objects of the eleventh magnitude. These values can be interpreted as the intrinsic accuracy of ASAS-3 data and correspond well to the values derived by Pigulski (2014). The relation between the standard deviation of the data fitted by the model described in Eq. 1 and the observed brightness in $V$ was fitted by the simple exponential $y=a+b\exp(x)$. Only 1 % of the fitted light curves exhibit standard deviations of the fit outside the $3\sigma_{\mathrm{exp}}$ interval (see Fig. 3), where $\sigma_{\mathrm{exp}}$ is the standard deviation derived from an exponential fit.

Photometric data for different stars from the ASAS survey are identified by a designation consisting of right ascension and declination (e.g., the light curve of HD 10081, the very first star from our sample, is designated ASAS J013615-6815.1). This identification, however, is not always sufficiently precise, and data from different stars can be blended, especially in high-density fields. In fact, this is the case for several stars of our sample, which in consequence exhibit inappropriately high standard deviations. To identify blended data, we separated the measurements from different data sets. Results for a prototypical star are shown in Fig. 5. In this particular case, the source coordinates of the different data sets are slightly different. The scatter in some of these data sets is significantly higher than the intrinsic accuracy of ASAS-3 data, which indicates blending issues and, possibly, the variability of another star in the same field of view.

2.5 Results

The nonlinear regression provides us with values of parameters and corresponding uncertainties. These values are derived under the assumption of a normal distribution of the fit residuals, and thus their determination does not have to be exact in cases of strongly nonlinear model functions. We therefore used the bootstrapping technique to determine corresponding error values and to verify the regression results. The results gained from both methods differ only slightly. Error values $\delta A_{1}$, $\delta A_{2}$, $\delta A_{3}$, and $\delta\varphi_{0}$ derived from the bootstrapping procedure reach, on average, 100 , 98 , 100  and 93 % of the values derived from the regression analysis.

As the values of the standard deviations for the corrected source data (i.e., data without blending issues) follow the intrinsic accuracy of the ASAS-3 data (Fig. 3), we can assume that the employed phenomenological model fits the data with high accuracy. The key outputs are the values of the model parameters. Obtained values of zero phase $\varphi_{0}$ are in agreement with the expectations; only in 7 % of all cases do the values lie outside the interval $[-0.05,0.05]$.

Let us assume that the values of the parameters $A_{1}$, $A_{2}$, and $A_{3}$ in Eq. 1 are significant only if their absolute values exceed three times their errors $\delta A_{i}$ as calculated using the bootstrapping technique. As stated above, we employ the term double wave if a light curve fitted with Eq. 1 contains two minima and has a significant value of parameter $A_{2}$. Similarly, the term single wave is reserved for stars with light curves characterized by a single minimum and a significant value of parameter $A_{1}$. The number of minima was determined individually for each given star by mathematically inspecting the local minima of the fitted light curve. These definitions of significance and wave character are used in the following to describe the different shapes of the mCP-star light curves.

The most common shape for a light curve among the photometrically variable mCP stars of our sample is the single wave, with 67 % of our sample stars showing this characteristic. This is illustrated in the upper panel of Fig. 6 (cf. also Fig. 7). It is furthermore apparent that the parameter $A_{1}$ is, in general, the main source of the effective semi-amplitude $A$. Furthermore, $A_{1}$ is significant in 98 % of all cases. The values tend to be negative as the light curve maxima are centered at $\varphi_{0}=0$. This might seem counterintuitive; however, we need to remember that the brightness maximum is defined by minimum magnitude. Also, 49 % of light curves show a symmetric single wave, while 18 % are characterized by an asymmetric single wave.

The middle panel of Fig. 6 shows the histogram of the normalized parameter $A_{2}$. Significant values of $A_{2}$ have been found for 46 % of our sample stars. Also, 30 % of all light curves are characterized by double waves; 15 % of our sample stars show symmetric double waves, while 14 % show asymmetric double waves; see Fig. 7 (the apparent inconsistency in expected equality of summed rate of symmetric and asymmetric double waves (29 %) and all double waves (30 %) is caused by rounding). It appears that 1 % of stars possess light curves with identical primary and secondary minima, in which case $A_{1}$ and $A_{3}$ are insignificant. However, we caution that the periods were derived from photometric observations only, and some period values may actually represent twice the true value, which is likely to have influenced this result. Without additional (spectroscopic) data, it is sometimes difficult to determine whether a light curve shows a double wave with identical minima or a single wave. Nevertheless, as the following analysis shows, double-wave light curves with identical minima are very rare. Therefore, the above described issue, if at all, applies only to a small portion of our sample stars and will not have influenced our results in a significant way.

The histogram of the values of the normalized parameter $A_{3}$, which seems to be significant in 36 % of all cases, appears to be symmetrically centered at zero (Fig. 6, bottom panel), which supports the claim that the observed antisymmetry is random. However, the distribution is slightly left-skewed ($-0.11\pm 0.09$).

The statistical distribution of the light curve shape according to wave character and symmetry is summarized in Fig. 7, while types and definitions are contained in Table 1. It becomes obvious that among the symmetric light curves, the single-wave character is highly dominant (77 % vs. 55 % among antisymmetric light curves). It must be noted that the category of light curves with two minima and insignificant $A_{2}$ (3 %) suffers from observations with high dispersion, and the corresponding values of $A_{2}$ are lower than their estimated errors. This is indicative of low-quality data, and we consequently did not include these light curves in the category of double-wave light curves. They are indicated as low-quality data in Fig. 7.

3 Simulations of symmetric spot distributions

If we assume that the main factor responsible for the distribution of chemical spots (which, as outlined in Sect. 1, correspond to the photometric spots; cf. Krtička et al. 2007 and Shulyak et al. 2010) is the magnetic field, we can expect some kind of correlation between the distribution of the spots and some magnetic field quantity. The recent study of Alecian (2015) shows that large over-abundances are expected near the magnetic equator because this region boasts almost horizontal magnetic field lines, which seems to be an important factor for the creation of surface chemical spots. We here try to confirm the anticipated relation between magnetic field and photometric spots employing the following model simulations.

The basic assumption is that the magnetic field of the model star is central, axially symmetric, and dipolar, with an inclination between rotational and magnetic axis $\beta$. We can then assume that the flux distribution can be represented by two circular spots located around the magnetic poles. We tried to simulate this by using circular spots of angular radius $\alpha=0.7$ rad (spots of medium size) on a surface grid system assuming random orientation of both rotational and magnetic axes. The surface grid was defined as a system of stellar meridians and parallels with a uniform grid step value of $\pi/150$ rad. For each grid node, the value of flux density was calculated and the total flux was integrated over the whole surface. An exemplary simulation is shown in Fig. 8. Parameter $\delta$ expresses the stellar latitude of the center of the spot and $i$ is the inclination of the rotational axis towards the observer. Random orientation of rotational and magnetic axes was established by choosing $\delta=\arcsin(\mathrm{rand}(0,1))$ and $i=\arccos(\mathrm{rand}(0,1))$, where $\mathrm{rand}(0,1)$ picks random numbers between 0 and 1 with uniform distribution. The value of the employed rotational phase step is 0.025. In our calculations, we took into account the limb-darkening formula $I(\rho)=I_{0}[1-q(1-\cos{\rho})]$ (Neilson & Lester 2011), where $q$ is a linear limb-darkening coefficient (here we use the value $q=0.5$), and $\rho$ is the angular distance from the center of the stellar disk.

At first, we assumed two completely dark spots centered at opposite longitudes and stellar latitude $\pm\delta$. The inclination of the stellar rotational axis $i$ is the angle between the rotational axis and the line of sight of the observer. As a result, we obtained a light curve fitted by the model function described in Eq. 1.

This simulation results in light curves that are always symmetric. Therefore, we removed the redundant antisymmetric part from Eq. 1. From light-curve fits, we obtained values of the parameters $A_{1}$ and $A_{2}$. In this way, a thousand random light curves were created.

To simplify the process, we assumed dark spots in our simulations, despite the fact that the photometric spots on mCP stars are usually bright in the optical region (Oksala et al. 2015). However, this should not pose a problem as the shape of a light curve containing a bright spot is simply a vertically inverted image of a light curve with a dark spot. This, therefore, does not influence the single- or double-wave character of the simulated light curves.

Figure 9 illustrates the dependence of the parameters $A_{1}$, $A_{2}$, and $A$ on the inclination of the rotation axis and the declination of the spots. We can see that the highest values of $A_{1}$ are derived for the combination $[\delta,i]=[45\degr,45\degr]$ and the highest values of $A_{2}$ for the combination $[\delta,i]=[0\degr,90\degr]$. The main result of this simulation is that double-wave light curves should occur with a probability of 79 %, which does not agree with the observed 77 % of single-wave light curves among the ASAS-3 mCP stars with symmetric light curves. There are at least two main factors which may have influenced these results. First, a double wave with identical minima can be misclassified as a single wave with half the true period. However, the simulation predicts that less than 9 % of cases satisfy the relation $|A_{1}/A_{2}|<0.1$, which we assume to be a satisfying condition for the identification of light curves with equal minima. Second, the spots are not completely dark, and some fainter spots will not have been detected. If we remove half of the cases with the lowest effective semi-amplitudes $A$, the occurrence rate of double-wave light curves reaches 86 %.

We ran similar simulations assuming spots with a radius of 0.3 rad, which resulted in double-wave light curves appearing in 74 % of cases up to 83 % after removal of half of the stars with the lowest effective amplitudes. However, for such small spots, values of $A$ only reach up to 0.1 mag, even if we assume the spots are completely dark. It is therefore unlikely that we observe spots of this size. Simulations assuming large spots of radius 1.2 rad resulted in 87 % of double-wave light curves (up to 95 % after removal of the lowest-amplitude objects). In addition, we carried out simulations assuming two spots with a radius of 0.7 rad, one being totally dark and the other one of random opacity. Similar results were obtained, with double wave light curves appearing in 74 % of cases (up to 88 % after removal of half of the stars with the lowest effective amplitudes). All studied cases are summarized in Table 2.

In summary, the results of our simulations suggest that, with the given assumptions, the light curves of mCP stars tend to be double-wave rather than single-wave. However, this is not compatible with the observations, which indicates that the model assuming similar distributions of magnetic field and photometric spots is not adequate. This is in agreement with the results of several studies employing Doppler mapping of magnetic fields in mCP stars and a comparison to the chemical abundance maps of different elements (e.g., Kochukhov et al. 2002, 2014, 2015).

The symmetry of the simulated light curves is a result of the chosen model. Real light curves are not always symmetric and the presence of nonzero parameter $A_{3}$ can be explained by noncircular spots or shifted spot location as compared to the simulations, which assumed that the spots are located opposite to each other.

4 Conclusions

Using archival time-series data from the ASAS-3 survey, we analyzed the sample of 650 ACV variables and candidates by Bernhard et al. (2015) and Hümmerich et al. (2016). We focused on the study of the general shapes of their light curves as relating to their symmetry and single- or double-wave character. The results show that 67 % of the light curves are single-wave, 30 % are double-wave, and asymmetry is found in 35 % of cases. Among the symmetric light curves, the percentage of single-wave light curves is even higher (77 %). We did not observe any kind of systematic antisymmetry.

We assumed a theoretical model of a symmetric dipole magnetic field with two opposite circular spots that follow the symmetry of the magnetic field and are hence located around the magnetic poles. Using this model, we made simulations assuming random positions of spots and random inclination of the rotational axis. Assuming completely dark, medium-sized identical spots with angular radii of 0.7 rad, we find an occurrence rate of 79 % for double-wave light curves. If we ignore the simulated light curves with the lowest amplitudes to take into account the lesser probability of their detection, the occurrence rate rises to 86 %. In cases of smaller spots with angular radii of 0.3 rad, similar results were obtained: 74 % of the light curves are double-wave, rising up to 83 % if low-amplitude light curves are ignored. However, the simulations show that the smaller spots frequently result in rotational modulation with amplitudes too low to be detectable in ASAS-3 data. Simulations for large spots with angular radii of 1.2 rad result in 87 % of light curves being double-wave, and up to 95 % after removal of half of the faintest cases.

In summary, the results obtained from our simulations are in contradiction with the observed light curves of mCP stars. While we have assumed quite simple initial conditions for our spot-modelling attempts, we do not see any reason to believe that our results are influenced by significant systematic error. In disagreement with the current understanding, we thereby conclude that the distribution of photometric spots does not follow the magnetic field topology.

Acknowledgements.

This research was supported by grant GA ČR 16-01116S.

Appendix A Fit parameters and ephemerides of the sample of 650 mCP stars.

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