NSV 1440: First WZ Sge-type Object in AM CVn stars and candidates

TL;DR

This paper reports the discovery of NSV 1440 as the first WZ Sge-type AM CVn star, showing unique early superhumps and rebrightenings, providing insights into its orbital period and mass ratio.

Contribution

It is the first to confirm an AM CVn star as WZ Sge-type with observed early superhumps, expanding understanding of these systems.

Findings

First observed early superhumps in an AM CVn star.

Estimated mass ratio q = 0.045, indicating a semi-degenerate secondary.

Detected multiple rebrightenings after superoutbursts.

Abstract

In 2015 and 2017, the AM CVn candidate NSV 1440 showed superoutbursts having the characteristic features of WZ Sge-type dwarf novae (DNe). By analogy with hydrogen-rich cataclysmic variables (CVs), we can interpret these outbursts as `double superoutbursts' which are composed of the first superoutburst with early superhumps and the second superoutburst with ordinary superhumps. The object also showed multiple rebrightenings after the main superoutbursts. Early superhumps had been never observed in AM CVn stars and candidates, thus NSV 1440 is the first confirmed WZ Sge-type AM CVn candidate. We obtained the early superhump period of 0.0252329(49) d and the growing (stage A) superhumps period of 0.025679(20) d from the 2015 superoutburst. We regarded the early superhump period as the orbital one. By using these periods we estimated the mass ratio $q = $0.045(2). This value suggests that NSV 1440 is indeed an AM CVn star and that the secondary is a semi-degenerate star.

Tables

Table 1. Table 1: List of the estimated periods.

	Period (day)	Date
2015
Early superhump∗	0.0252329(49)	0.891–4.769
Stage A	0.025679(20)	6.872–8.082
Stage B	0.025356(2)	8.522–12.082
Fading stage	0.025211(16)	12.177–14.786
Late stage	0.0254019(4)	14.850–64.348
2017
Stage A	0.02562(21)	7.790–7.899
Stage B	0.0253478(17)	8.787–11.897
Fading stage	0.02531(17)	12.776–12.903
Late stage	0.0253926(7)	14.770–29.892
∗  We use the early superhump period as $P_{\mathrm{orb}}$.

Table 2. Table E1: Log of observations of NSV 1440 in 2015

Start ∗	End ∗	Mag†	${\sigma }_{\mathrm{Mag}}$‡	$N$§	Obs∥
0.8898	1.0540	12.998	0.002	65	HaC
1.8870	2.0904	13.137	0.002	85	HaC
2.5267	2.7838	0.372	0.001	733	MLF
2.8842	3.0924	13.248	0.003	87	HaC
3.3320	3.4302	13.398	0.001	100	SPET
3.5174	3.6244	0.500	0.001	309	MLF
3.8813	4.0827	13.376	0.002	84	HaC
4.2724	4.3770	13.487	0.001	100	SPET
4.5354	4.7701	0.674	0.002	676	MLF
4.8785	5.0849	14.267	0.019	86	HaC
5.2262	5.3156	14.804	0.010	100	COO
5.2483	5.4314	15.262	0.012	154	SPET
5.8758	6.0843	17.085	0.048	86	HaC
6.8731	7.0832	16.084	0.022	70	HaC
7.5648	7.8429	0.836	0.005	802	MLF
7.8704	8.0834	13.465	0.004	115	HaC
8.5238	8.7154	0.604	0.002	552	MLF
8.8675	9.0839	13.481	0.004	118	HaC
10.0357	10.0840	13.665	0.005	29	HaC
10.5446	10.8418	0.916	0.001	855	MLF
11.8599	12.0832	13.959	0.003	120	HaC
12.2777	12.2777	14.153	–	1	SPET
12.8571	13.0825	15.720	0.012	123	HaC
13.2295	13.3184	15.920	0.008	98	COO
13.5190	13.6784	3.160	0.005	401	MLF
13.8544	14.0833	16.084	0.008	125	HaC
14.1800	14.4771	16.225	0.003	315	MGW
14.2019	14.2837	16.082	0.006	93	COO
14.5276	14.7287	3.369	0.003	576	MLF
14.8515	15.0831	16.340	0.006	174	HaC
15.1737	15.4781	16.321	0.003	322	MGW
15.5221	15.6718	3.353	0.005	361	MLF
15.8489	16.0828	16.209	0.004	156	HaC
16.1631	16.4782	16.200	0.003	346	MGW
16.6098	16.8054	3.266	0.003	561	MLF
16.8461	17.0470	16.063	0.005	133	HaC
17.7688	17.8459	1.422	0.003	222	MLF
∗BJD$-$2457346.751 (same as figure 1, 3 and E1
†Mean magnitude. All observations are no filter (clear).
†Standard deviation of the observed magnitude.
§Number of observations.
∥Observer’s code: HaC(F.-J. Hambsch), MLF (B. Monard),
MGW(G. Myers), SPET(P. Starr), COO(L. M. Cook)

Table 3. Table E1: Log of observations of NSV 1440 in 2015 (continued)

Start ∗	End ∗	Mag†	${\sigma }_{\mathrm{Mag}}$‡	$N$§	Obs∥
17.8433	18.0439	14.546	0.011	122	HaC
18.8405	19.0404	16.448	0.009	124	HaC
19.8378	20.0388	16.529	0.007	125	HaC
20.2918	20.4782	16.484	0.003	214	MGW
20.5318	20.8392	3.514	0.002	878	MLF
20.8350	21.0360	16.455	0.006	125	HaC
21.8322	22.0319	16.607	0.007	120	HaC
22.2789	22.4782	16.564	0.004	244	MGW
22.8294	22.8473	16.599	0.026	9	HaC
23.2991	23.4568	16.440	0.003	164	MGW
23.8266	24.0277	16.414	0.009	123	HaC
24.2995	24.3904	16.324	0.004	115	MGW
24.5284	24.8259	2.061	0.025	827	MLF
24.8239	25.0247	14.368	0.009	123	HaC
25.5257	25.5913	2.859	0.009	58	MLF
25.8211	26.0214	16.509	0.010	123	HaC
26.8183	27.0186	16.695	0.010	119	HaC
27.2992	27.4784	16.670	0.004	213	MGW
27.5710	27.8199	3.752	0.005	353	MLF
27.9891	28.0160	16.590	0.020	19	HaC
28.3005	28.4782	16.547	0.005	106	MGW
28.5371	28.8419	3.069	0.009	431	MLF
28.8133	29.0129	16.356	0.010	121	HaC
29.3037	29.4775	16.473	0.005	175	MGW
29.8105	30.0106	16.594	0.016	121	HaC
30.2989	30.4215	16.606	0.005	119	MGW
30.8084	31.0071	16.548	0.017	74	HaC
31.8051	32.0047	15.364	0.067	86	HaC
32.5268	32.8433	2.488	0.007	907	MLF
32.8383	33.0023	15.943	0.016	75	HaC
33.2758	33.3766	16.825	0.082	2	SPET
33.5329	33.7819	3.851	0.006	352	MLF
35.2284	35.2284	16.701	–	1	SPET
35.4451	35.4665	16.591	0.036	25	COO
36.5335	36.8398	3.123	0.012	433	MLF
37.6134	37.8440	3.639	0.005	326	MLF
38.2401	38.4775	16.884	0.008	280	MGW
38.2818	38.2818	16.755	–	1	SPET
38.7856	38.9860	16.601	0.016	76	HaC
39.3522	39.3522	16.674	–	1	SPET
39.4124	39.4778	16.637	0.007	81	MGW
39.7829	39.9810	15.389	0.080	63	HaC
40.2406	40.4519	14.697	0.010	225	MGW

Table 4. Table E1: Log of observations of NSV 1440 in 2015 (continued)

Start ∗	End ∗	Mag†	${\sigma }_{\mathrm{Mag}}$‡	$N$§	Obs∥
40.4201	40.4201	14.942	0.003	2	SPET
40.7802	40.9804	15.923	0.018	62	HaC
41.2516	41.4007	16.733	0.005	161	MGW
41.7775	41.9782	16.769	0.019	55	HaC
42.7766	42.9778	16.769	0.017	55	HaC
44.7712	44.9718	16.754	0.014	55	HaC
45.7628	45.9666	16.805	0.011	79	HaC
46.7644	46.9652	16.800	0.010	77	HaC
47.7702	47.9638	16.640	0.013	53	HaC
48.2146	48.4468	15.436	0.003	282	MGW
49.7638	49.9580	16.770	0.018	56	HaC
50.2256	50.4782	16.856	0.004	193	MGW
53.2775	53.4783	16.896	0.003	225	MGW
57.1948	57.3692	16.562	0.004	219	MGW
58.1977	58.4472	15.420	0.010	287	MGW
64.1787	64.3493	16.731	0.005	210	MGW

Table 5. Table E2: Log of observations of NSV 1440 in 2017

Start ∗	End ∗	Mag†	${\sigma }_{\mathrm{Mag}}$‡	$N$§	Obs∥
5.7946	5.8998	14.274	0.009	44	HaC
6.7918	6.8995	15.416	0.011	45	HaC
7.7885	7.8979	13.302	0.003	82	HaC
8.7857	8.8978	13.393	0.003	84	HaC
9.5052	9.6732	0.624	0.001	484	MLF
9.7823	9.8979	13.538	0.003	103	HaC
10.7800	10.8965	13.675	0.003	95	HaC
11.3870	11.6694	0.918	0.001	807	MLF
11.7772	11.8962	13.828	0.002	97	HaC
12.7744	12.9023	14.108	0.007	105	HaC
13.7716	13.9018	15.973	0.010	105	HaC
14.7689	14.9003	16.184	0.010	98	HaC
15.7663	15.9000	16.249	0.008	86	HaC
16.7636	16.8988	16.222	0.007	87	HaC
17.7608	17.8988	14.229	0.005	89	HaC
19.7553	19.8975	16.566	0.013	92	HaC
20.7246	20.8958	16.400	0.022	76	HaC
21.7218	21.8959	16.457	0.012	77	HaC
25.3862	25.6586	2.588	0.007	758	MLF
25.7684	25.8820	16.065	0.012	64	HaC
26.7656	26.8219	16.670	0.033	28	HaC
28.7600	28.8910	16.515	0.009	77	HaC
29.7573	29.8910	16.488	0.008	78	HaC
32.9011	32.9018	15.777	0.176	2	HaC
33.9004	33.9011	16.713	0.121	2	HaC
34.8998	34.9006	16.710	0.049	2	HaC
35.8990	35.8997	16.585	0.047	2	HaC
36.8983	36.8991	16.733	0.199	2	HaC
37.8976	37.8976	16.551	–	1	HaC
38.8970	38.8970	16.670	–	1	HaC
39.8944	39.8952	14.891	0.006	2	HaC
40.8903	40.8910	15.913	0.046	2	HaC
41.3925	41.5975	3.957	0.005	510	MLF
41.8896	41.8903	16.777	0.171	2	HaC
42.8889	42.8897	16.868	0.182	2	HaC
43.8882	43.8889	16.759	0.015	2	HaC
44.8875	44.8882	16.665	0.011	2	HaC
∗BJD$-$2457982.000 (same as figure 1 and 3
†Mean magnitude. All observations are no filter (clear).
†Standard deviation of the observed magnitude.
§Number of observations.
∥Observer’s code: HaC(F.-J. Hambsch), MLF (B. Monard),
MGW(G. Myers), SPET(P. Starr), COO(L. M. Cook)

Table 6. Table E2: Log of observations of NSV 1440 in 2017 (continued)

Start ∗	End ∗	Mag†	${\sigma }_{\mathrm{Mag}}$‡	$N$§	Obs∥
45.8868	45.8875	16.726	0.051	2	HaC
46.8861	46.8869	16.815	0.023	2	HaC
47.8854	47.8862	16.697	0.091	2	HaC
48.8847	48.8855	15.685	0.068	2	HaC
49.8840	49.8848	15.976	0.090	2	HaC
50.8833	50.8841	16.489	0.012	2	HaC
51.8826	51.8834	16.604	0.210	2	HaC
52.8820	52.8827	16.841	0.125	2	HaC
53.8812	53.8820	16.546	0.009	2	HaC
54.8805	54.8813	16.529	0.086	2	HaC
55.8799	55.8806	16.531	0.080	2	HaC
56.8791	56.8799	15.122	0.008	2	HaC
57.8793	57.8793	17.926	–	1	HaC
58.8777	58.8785	16.718	0.190	2	HaC
59.8771	59.8778	16.812	0.014	2	HaC
60.8763	60.8771	16.955	0.163	2	HaC
61.8757	61.8764	16.825	0.103	2	HaC
62.8750	62.8757	16.812	0.166	2	HaC
63.8743	63.8751	16.824	0.142	2	HaC
64.8736	64.8743	16.719	0.020	2	HaC
65.8728	65.8736	16.655	0.044	2	HaC
66.8722	66.8730	16.689	0.090	2	HaC
67.8715	67.8722	14.906	0.018	2	HaC
68.8715	68.8722	16.942	0.140	2	HaC
69.8708	69.8715	16.970	0.104	2	HaC
70.8702	70.8709	16.777	0.082	2	HaC
71.8694	71.8701	17.052	0.250	2	HaC
72.8688	72.8695	16.920	0.139	2	HaC
73.8680	73.8687	16.940	0.040	2	HaC
74.8681	74.8688	17.016	0.088	2	HaC
75.8674	75.8681	16.809	0.164	2	HaC
76.8667	76.8674	16.901	0.113	2	HaC
77.8659	77.8667	16.988	0.088	2	HaC
78.8660	78.8667	17.099	0.495	2	HaC
79.8653	79.8660	15.047	0.037	2	HaC
80.8646	80.8653	16.910	0.030	2	HaC
81.8639	81.8646	16.958	0.251	2	HaC
82.6613	82.6621	16.957	0.113	2	HaC
83.6586	83.6593	16.945	0.020	2	HaC
84.6558	84.6566	17.101	0.173	2	HaC
85.3592	85.4434	4.394	0.011	193	MLF
85.6530	85.6537	17.335	0.180	2	HaC
86.6502	86.6509	17.080	0.033	2	HaC

Table 7. Table E2: Log of observations of NSV 1440 in 2017 (continued)

Start ∗	End ∗	Mag†	${\sigma }_{\mathrm{Mag}}$‡	$N$§	Obs∥
87.6475	87.6482	17.247	0.049	2	HaC
88.6447	88.6454	17.172	0.326	2	HaC
89.6419	89.6426	17.245	0.222	2	HaC
90.6391	90.6398	17.017	0.034	2	HaC
91.6363	91.6371	17.209	0.118	2	HaC
92.6336	92.6343	17.052	0.060	2	HaC
93.6307	93.6314	17.212	0.247	2	HaC
94.6279	94.6287	17.276	0.096	2	HaC
95.6252	95.6259	17.181	0.044	2	HaC
96.6224	96.6231	17.173	0.156	2	HaC
97.6197	97.6204	17.237	0.164	2	HaC
98.6169	98.6176	17.326	0.055	2	HaC
99.6142	99.6149	17.835	0.132	2	HaC
100.6120	100.6128	17.216	0.039	2	HaC
101.6093	101.6100	17.221	0.070	2	HaC
102.6065	102.6072	17.676	0.175	2	HaC
103.6037	103.6044	17.229	0.058	2	HaC
104.6008	104.6016	17.435	0.461	2	HaC
105.5981	105.5988	17.258	0.250	2	HaC
106.5953	106.5960	17.167	0.210	2	HaC
107.5926	107.5933	17.446	0.021	2	HaC
108.5899	108.5906	17.193	0.002	2	HaC
109.5870	109.5877	16.945	0.241	2	HaC
111.5815	111.5822	17.725	0.234	2	HaC
113.5759	113.5767	17.968	0.194	2	HaC
114.5732	114.5739	18.137	0.137	2	HaC
115.5704	115.5711	17.611	0.060	2	HaC
116.5676	116.5684	18.074	0.186	2	HaC
117.5648	117.5655	17.839	0.136	2	HaC
118.5620	118.5628	18.186	0.224	2	HaC
119.5592	119.5600	18.203	0.189	2	HaC
120.5565	120.5572	18.481	0.097	2	HaC
121.5538	121.5545	18.453	0.254	2	HaC
122.5516	122.5524	17.954	0.265	2	HaC
125.5578	125.5586	18.803	0.426	2	HaC
126.5558	126.5565	18.530	0.096	2	HaC
127.5537	127.5537	18.328	–	1	HaC
128.5503	128.5510	18.204	0.139	2	HaC
131.5410	131.5410	18.045	–	1	HaC
133.5347	133.5347	18.407	–	1	HaC
137.5244	137.5244	17.673	–	1	HaC
142.5126	142.5126	18.037	–	1	HaC

Table 8. Table E3: Timings of superhump maxima of NSV 1440 in 2015.

$E$	Maximum time∗	Error	$O-C$†	$N$‡
0	7.03553	0.00068	-0.00798	7
1	7.05998	0.00058	-0.00890	7
21	7.57272	0.00061	-0.00330	47
24	7.65045	0.00051	-0.00164	60
25	7.67702	0.00050	-0.00044	58
26	7.70118	0.00061	-0.00162	58
27	7.72639	0.00042	-0.00178	58
28	7.75210	0.00053	-0.00143	59
29	7.78111	0.00097	0.00223	58
30	7.80405	0.00046	-0.00019	58
31	7.82826	0.00049	-0.00134	59
38	8.00756	0.00106	0.00046	12
59	8.54141	0.00019	0.00180	58
60	8.56712	0.00016	0.00215	58
61	8.59260	0.00018	0.00227	58
62	8.61800	0.00022	0.00232	59
63	8.64317	0.00019	0.00214	59
64	8.66806	0.00021	0.00166	58
65	8.69376	0.00019	0.00201	58
73	8.89717	0.00082	0.00255	12
76	8.97323	0.00037	0.00254	11
79	9.04841	0.00064	0.00165	11
139	10.57123	0.00039	0.00302	59
140	10.59640	0.00034	0.00283	59
141	10.62099	0.00035	0.00207	58
142	10.64665	0.00024	0.00237	59
143	10.67219	0.00029	0.00255	59
144	10.69760	0.00021	0.00260	58
145	10.72232	0.00047	0.00196	59
146	10.74784	0.00035	0.00212	59
147	10.77259	0.00035	0.00152	59
148	10.79878	0.00035	0.00235	58
149	10.82362	0.00035	0.00183	59
191	11.88719	0.00078	0.00038	12
192	11.91419	0.00091	0.00202	10
193	11.93871	0.00061	0.00119	10
194	11.96480	0.00038	0.00193	12
195	11.98758	0.00089	-0.00066	11
196	12.01453	0.00089	0.00093	12
197	12.04180	0.00066	0.00285	11
230	12.88009	0.00088	0.00434	9
∗BJD$-$2457346.751 (same as figure 1 and 3).
†$C=2457353.794513+0.02535754750E$.
‡Number of points used to determine the maximum.

Table 9. Table E3: Timings of superhump maxima of NSV 1440 in 2015 (continued).

$E$	Maximum time∗	Error	$O-C$†	$N$‡
232	12.92823	0.00084	0.00176	10
233	12.95554	0.00054	0.00371	12
234	12.98005	0.00064	0.00287	12
235	13.00527	0.00053	0.00274	11
236	13.03049	0.00094	0.00260	11
237	13.05637	0.00049	0.00312	12
244	13.23305	0.00053	0.00230	20
245	13.25899	0.00040	0.00288	23
246	13.28529	0.00100	0.00382	21
247	13.30968	0.00105	0.00285	18
256	13.53975	0.00047	0.00470	54
257	13.56191	0.00041	0.00151	49
259	13.60964	0.00101	-0.00148	59
261	13.66484	0.00060	0.00301	54
283	14.21677	0.00040	-0.00293	47
284	14.24298	0.00040	-0.00208	48
287	14.31922	0.00309	-0.00191	25
288	14.34528	0.00112	-0.00121	24
289	14.37048	0.00112	-0.00137	24
290	14.39580	0.00122	-0.00140	24
292	14.44656	0.00078	-0.00136	24
293	14.47320	0.00098	-0.00007	19
296	14.54730	0.00130	-0.00205	59
297	14.57497	0.00094	0.00026	56
298	14.59405	0.00087	-0.00601	59
299	14.61735	0.00086	-0.00807	58
300	14.64042	0.00641	-0.01036	58
301	14.67064	0.00067	-0.00550	58
302	14.70126	0.00134	-0.00024	59
322	15.20068	0.00060	-0.00796	26
323	15.22620	0.00109	-0.00780	25
327	15.32919	0.00099	-0.00624	25
328	15.35461	0.00168	-0.00618	25
329	15.37861	0.00232	-0.00754	25
331	15.43101	0.00057	-0.00585	26
332	15.45570	0.00080	-0.00652	25
336	15.55663	0.00082	-0.00702	41
337	15.58332	0.00096	-0.00569	45
338	15.60673	0.00106	-0.00763	58
339	15.63103	0.00064	-0.00869	49
340	15.65951	0.00096	-0.00557	55
349	15.88843	0.00106	-0.00487	15
353	15.98966	0.00082	-0.00507	15
354	16.01330	0.00078	-0.00679	14

Table 10. Table E3: Timings of superhump maxima of NSV 1440 in 2015 (continued).

$E$	Maximum time∗	Error	$O-C$†	$N$‡
355	16.03913	0.00089	-0.00632	14
356	16.06652	0.00088	-0.00428	14
361	16.19323	0.00044	-0.00436	25
362	16.21864	0.00048	-0.00431	26
363	16.24375	0.00094	-0.00456	26
366	16.31962	0.00046	-0.00476	25
367	16.34620	0.00076	-0.00353	25
368	16.37098	0.00040	-0.00411	26
369	16.39607	0.00052	-0.00438	26
370	16.42090	0.00071	-0.00490	25
371	16.44703	0.00035	-0.00413	26
378	16.62417	0.00077	-0.00449	58
379	16.64643	0.00125	-0.00759	58
380	16.67116	0.00078	-0.00822	58
381	16.70058	0.00114	-0.00416	58
382	16.72708	0.00097	-0.00302	58
383	16.75134	0.00095	-0.00412	58
384	16.77798	0.00051	-0.00283	58
389	16.90430	0.00076	-0.00330	14
392	16.98097	0.00169	-0.00270	14
394	17.02965	0.00103	-0.00474	15
523	20.30808	0.00082	0.00257	26
524	20.33344	0.00104	0.00257	26
525	20.35825	0.00087	0.00202	25
526	20.38164	0.00092	0.00006	25
527	20.40691	0.00044	-0.00003	22
529	20.45956	0.00119	0.00191	26
546	20.89078	0.00057	0.00204	11
547	20.91461	0.00091	0.00051	13
601	22.29049	0.00048	0.00709	25
602	22.31738	0.00080	0.00863	25
603	22.34062	0.00081	0.00651	25
604	22.36770	0.00087	0.00823	25
605	22.39283	0.00070	0.00800	24
606	22.41751	0.00112	0.00732	24
607	22.44401	0.00062	0.00846	25
608	22.46759	0.00054	0.00669	23
641	23.30594	0.00051	0.00824	25
642	23.33218	0.00040	0.00912	26
643	23.35865	0.00042	0.01023	26
662	23.83888	0.00099	0.00867	7
664	23.88559	0.00052	0.00467	12
681	24.32273	0.00052	0.01072	26
682	24.34793	0.00048	0.01057	25

Table 11. Table E3: Timings of superhump maxima of NSV 1440 in 2015 (continued).

$E$	Maximum time∗	Error	$O-C$†	$N$‡
683	24.37235	0.00059	0.00963	25
799	27.32055	0.00052	0.01636	24
800	27.34656	0.00066	0.01701	24
801	27.37153	0.00043	0.01662	24
802	27.39701	0.00036	0.01674	24
803	27.42265	0.00041	0.01703	24
804	27.44837	0.00063	0.01738	23
805	27.47338	0.00069	0.01704	17
810	27.60095	0.00064	0.01782	29
811	27.62675	0.00085	0.01827	28
812	27.65198	0.00087	0.01814	29
813	27.67551	0.00065	0.01631	29
814	27.70230	0.00078	0.01774	29
815	27.72874	0.00110	0.01882	29
817	27.78457	0.00207	0.02394	29
818	27.80378	0.00056	0.01780	29
838	28.31031	0.00074	0.01717	22
843	28.43813	0.00058	0.01820	21
844	28.46245	0.00066	0.01716	22
855	28.73965	0.00085	0.01543	29
856	28.76774	0.00065	0.01816	29
857	28.79029	0.00120	0.01536	28
858	28.82008	0.00267	0.01979	35
878	29.32823	0.00090	0.02079	21
879	29.35354	0.00075	0.02074	21
880	29.37978	0.00061	0.02162	20
881	29.40311	0.00028	0.01960	21
882	29.42966	0.00076	0.02079	20
883	29.45506	0.00086	0.02083	19
898	29.83663	0.00365	0.02204	9
900	29.88182	0.00122	0.01651	12
902	29.93984	0.00141	0.02382	13
904	29.98983	0.00081	0.02310	13
917	30.31616	0.00072	0.01977	25
918	30.34502	0.00052	0.02328	25
919	30.36800	0.00051	0.02090	23
1006	32.57241	0.00047	0.01920	59
1007	32.59711	0.00076	0.01855	58
1008	32.62250	0.00069	0.01858	58
1009	32.65006	0.00115	0.02078	58
1010	32.67470	0.00085	0.02006	58
1011	32.70033	0.00052	0.02033	59
1012	32.72316	0.00106	0.01781	59
1013	32.74884	0.00058	0.01813	58

Table 12. Table E3: Timings of superhump maxima of NSV 1440 in 2015 (continued).

$E$	Maximum time∗	Error	$O-C$†	$N$‡
1014	32.77472	0.00089	0.01865	58
1015	32.80402	0.00089	0.02260	58
1016	32.82728	0.00088	0.02050	58
1162	36.54211	0.00108	0.03313	28
1163	36.56420	0.00149	0.02985	28
1164	36.59776	0.00303	0.03806	29
1165	36.61692	0.00094	0.03186	28
1166	36.63856	0.00146	0.02814	28
1167	36.66798	0.00182	0.03220	27
1168	36.68965	0.00060	0.02852	29
1169	36.71854	0.00090	0.03206	29
1170	36.74117	0.00090	0.02933	29
1205	37.63432	0.00070	0.03496	29
1206	37.65766	0.00085	0.03295	29
1207	37.68302	0.00108	0.03295	29
1208	37.70748	0.00031	0.03205	28
1209	37.73136	0.00199	0.03057	29
1210	37.75901	0.00093	0.03287	28
1211	37.78580	0.00176	0.03429	29
1212	37.81117	0.00129	0.03431	28
1213	37.83164	0.00124	0.02942	27
1236	38.41839	0.00139	0.03295	24
1237	38.44155	0.00092	0.03076	25
1238	38.46594	0.00271	0.02978	25
1309	40.26518	0.00105	0.02864	23
1311	40.31788	0.00129	0.03062	22
1312	40.34172	0.00192	0.02911	23
1315	40.42033	0.00103	0.03164	24
1348	41.25810	0.00064	0.03261	20
1349	41.28359	0.00076	0.03275	23
1350	41.31109	0.00149	0.03489	23
1351	41.33288	0.00085	0.03132	22
1352	41.36051	0.00101	0.03360	23
1353	41.38411	0.00060	0.03184	17
1526	45.77633	0.00303	0.03720	13
1625	48.29053	0.00140	0.04100	26
1626	48.31561	0.00139	0.04072	27
1627	48.34478	0.00124	0.04454	25
1823	53.32038	0.00067	0.05006	25
1824	53.34916	0.00064	0.05348	26
1828	53.44638	0.00080	0.04927	25
1978	57.24552	0.00083	0.04478	26
1979	57.27226	0.00265	0.04616	26
1980	57.29554	0.00070	0.04408	26

Table 13. Table E3: Timings of superhump maxima of NSV 1440 in 2015 (continued).

$E$	Maximum time∗	Error	$O-C$†	$N$‡
1981	57.32261	0.00171	0.04580	26
2016	58.21708	0.00049	0.05275	25
2017	58.24373	0.00136	0.05404	26
2018	58.26918	0.00102	0.05414	25
2019	58.29248	0.00037	0.05207	26
2020	58.31870	0.00034	0.05294	25
2021	58.34415	0.00047	0.05303	26
2022	58.36952	0.00042	0.05305	25
2023	58.39516	0.00059	0.05333	22
2251	64.18447	0.00064	0.06112	23
2252	64.20992	0.00117	0.06121	24
2255	64.28665	0.00140	0.06187	26
2256	64.31203	0.00118	0.06189	25
2257	64.33610	0.00119	0.06060	24

Table 14. Table E4: Timings of superhump maxima of NSV 1440 in 2017.

$E$	Maximum time∗	Error	$O-C$†	$N$‡
30	7.79878	0.00067	-0.00532	16
31	7.82167	0.00071	-0.00778	15
32	7.84789	0.00070	-0.00693	15
33	7.87355	0.00048	-0.00662	15
34	7.89908	0.00098	-0.00645	9
70	8.81625	0.00050	-0.00215	15
71	8.84228	0.00070	-0.00148	15
72	8.86629	0.00098	-0.00283	15
73	8.89179	0.00044	-0.00268	15
98	9.52667	0.00029	-0.00174	58
99	9.55158	0.00026	-0.00219	58
100	9.57734	0.00032	-0.00179	58
101	9.60212	0.00025	-0.00237	58
102	9.62767	0.00023	-0.00217	58
103	9.65369	0.00027	-0.00151	58
109	9.80509	0.00118	-0.00226	17
110	9.83168	0.00108	-0.00103	18
111	9.85618	0.00080	-0.00189	18
112	9.88081	0.00048	-0.00261	17
149	10.82032	0.00119	-0.00133	17
150	10.84469	0.00049	-0.00231	16
151	10.87055	0.00044	-0.00181	15
172	11.40200	0.00034	-0.00288	58
173	11.42743	0.00038	-0.00280	56
174	11.45236	0.00034	-0.00323	59
175	11.47869	0.00048	-0.00226	57
176	11.50452	0.00029	-0.00178	58
177	11.52973	0.00052	-0.00193	58
178	11.55450	0.00048	-0.00252	59
179	11.57972	0.00034	-0.00265	57
180	11.60529	0.00038	-0.00244	58
181	11.63030	0.00030	-0.00278	58
182	11.65545	0.00047	-0.00300	57
187	11.78264	0.00052	-0.00260	15
188	11.80732	0.00054	-0.00327	18
189	11.83251	0.00052	-0.00344	15
190	11.86024	0.00121	-0.00106	16
191	11.88319	0.00112	-0.00347	15
227	12.79641	0.00056	-0.00313	19
228	12.82239	0.00036	-0.00250	16
∗BJD$-$2457982.000 (same as figure 1 and 3).
†$C=2457996.842150+0.02535754750E$.
‡Number of points used to determine the maximum.

Table 15. Table E4: Timings of superhump maxima of NSV 1440 in 2017 (continued).

$E$	Maximum time∗	Error	$O-C$†	$N$‡
229	12.84706	0.00050	-0.00319	16
230	12.87103	0.00067	-0.00458	16
231	12.89907	0.00047	-0.00190	13
266	13.78420	0.00084	-0.00428	19
267	13.81098	0.00090	-0.00286	16
268	13.83904	0.00237	-0.00015	15
269	13.86463	0.00101	0.00008	16
270	13.88976	0.00113	-0.00015	15
346	15.80863	0.00226	-0.00846	12
347	15.83535	0.00155	-0.00709	12
724	25.40132	0.00057	-0.00092	59
725	25.42540	0.00069	-0.00219	59
726	25.44882	0.00167	-0.00413	57
727	25.47992	0.00157	0.00161	59
728	25.50450	0.00089	0.00083	58
729	25.52809	0.00099	-0.00094	59
730	25.55569	0.00116	0.00130	58
731	25.58045	0.00084	0.00071	58
739	25.78447	0.00196	0.00187	10
740	25.80980	0.00653	0.00184	9
741	25.83844	0.00077	0.00513	12
857	28.78673	0.00060	0.01194	10
858	28.81273	0.00085	0.01258	10
859	28.83715	0.00485	0.01164	13
860	28.86360	0.00104	0.01274	14
897	29.80434	0.00150	0.01525	10
898	29.82538	0.00281	0.01093	13
899	29.85278	0.00144	0.01297	13

Equations

$$M_2=1.43\times 10^{-4}{P}_{\mathrm{orb}}^{-1.22}\mathrm{for}\mathrm{the}\mathrm{fully}\text{mathchar}45degenerate\mathrm{secondary},$$

$$M_2=3.18\times 10^{-4}{P}_{\mathrm{orb}}^{-1.27}\mathrm{for}\mathrm{the}\mathrm{semi}\text{mathchar}45degenerate\mathrm{secondary},$$

$$\Delta T[\mathrm{day}]=1.53\times 10^{-9}{P}_{\mathrm{orb}}{[\min ]}^{7.35}+\mathrm{24.7.}$$

Full text

1 Introduction

AM CVn stars are a subclass of cataclysmic variables (CVs), which are close binary systems composed of a white dwarf (WD) primary and a mass-transferring secondary. Their secondary stars are helium stars or helium WDs. They are characterized by absences of hydrogen lines in their spectra and their ultra-short orbital periods of 5–65 min (for reviews of AM CVn stars, see [Nelemans (2005), Solheim (2010)]).

Outbursts in AM CVn stars are theoretically studied by Tsugawa, Osaki (1997) and are basically understood by analogy with the thermal instability model in H-rich dwarf novae (DNe). However, the outburst behaviors of AM CVn stars are complicated, e.g. dips, rebrightenings and so on. Kotko et al. (2012) argued that variation of the mass-transfer rate, may be caused by irradiation of the secondary, is necessary for reproducing their light curves on the basis of their model calculation. Warner (1995) and Warner (2015) interpreted the typical outbursting AM CVn stars as VY Scl-type objects, which show brightness variations owing to the change of the mass-transfer rate. More detailed observational studies are required to understand the outburst mechanism and the stability of the mass-transfer rate.

Some AM CVn stars show not only normal outbursts but also superoutbursts with superhumps (Patterson et al., 1993; Warner, 1995). Superhumps are small-amplitude modulations whose period $P_{\rm SH}$ is a few percent longer than the orbital period $P_{\rm orb}$. Superoutbursts and superhumps are characteristic phenomena of SU UMa-type DNe and are explained by the thermal-tidal instability (TTI) model (Osaki, 1989). When an outer disk reaches the 3:1 resonance radius, the disk becomes eccentric and begin to show periodic modulations, i.e. superhumps (Whitehurst, 1988; Lubow, 1991a, b; Hirose, Osaki, 1990). Kato et al. (2014) and Isogai et al. (2016) confirmed that the period variations of superhumps in AM CVn stars are consistent with those in H-rich DNe, and proposed that the superoutbursts in AM CVn stars are also interpreted by the TTI model.

AM CVn stars typically have an extreme low mass secondary (cf. Nelemans et al. (2001)). We know that $P_{\rm orb}$ of outbursting AM CVn stars are typically longer than 1300 s $\sim$ 0.015 d (Solheim, 2010), and that $M_{1}$ of $0.65M_{\odot}$ is often used (e.g. Bildsten et al. (2006)). From these values and the theoretical evolutionary tracks (see section 5.3 and equation 1 and 2), we can approximately estimate that $q$ of typical outbursting AM CVn stars are less than 0.1.

Because disks in CVs with $q<$ 0.25–0.30 can reach the 3:1 resonance radius, many outbursting AM CVn stars can show superhumps.

Many hydrogen-rich DNe with $q<0.09$ are known as WZ Sge-type DNe, which are a subclass of SU UMa-type DNe. It is known that WZ Sge-type DNe show longer and larger superoutburst in comparison with SU UMa-type DNe and show few normal outbursts (for a review of WZ Sge-type DNe, see Kato (2015)). The analogy between WZ Sge-type DNe and some AM CVn stars has sometimes been discussed. For instance, Nogami et al. (2004) pointed out that the outburst behavior of V406 Hya resembles with that of the WZ Sge-type star EG Cnc in that the object showed the multiple rebrightenings after the main superoutburst. Levitan et al. (2015) proposed that the long $P_{\rm orb}$ systems have low mass-transfer rates and will show rare and large outbursts. Thus, they indicated that such objects may be WZ Sge-type AM CVn stars. To date, “WZ Sge-type” in AM CVn stars has basically meant that an object shows multiple rebrightenings or that an object shows rare and larger-scale superoutbursts.

The larger-scale WZ Sge-type superoutbursts are explained by the presence of the 2:1 resonance. If a system has extreme low mass ratio and enough mass is accumulated in the disk, the outer edge of the disk can reach the 2:1 resonance radius beyond the 3:1 one (Osaki, Meyer, 2002). The two-armed dissipation pattern in the disk is caused by the 2:1 resonance, then the early superhumps begin to grow (Lin, Papaloizou, 1979). Because the 2:1 resonance suppresses the 3:1 resonance (Lubow, 1991a; Osaki, Meyer, 2003), ordinary superhumps begin to grow after the end of the early superhump phase. It is widely known that early superhumps have double-wave profiles and the periods are close to $P_{\rm orb}$ (Kato, 2002). For instance, Ishioka et al. (2002) have confirmed that the early superhump period of AL Com is 0.05 $\%$ shorter than $P_{\rm orb}$. Patterson et al. (2002) also proposed that the signal of the early superhumps in WZ Sagittae is “essentially consistent with orbital frequency”. It is considered that a vertical extended disk originates such modulations. Thus, early superhumps are only observed in high-inclination systems. On the other hands, low-inclination systems show a long plateau phase with no superhumps which is brighter than the superoutburst plateau with ordinary superhumps. Such a plateau phase is also regarded as a kind of early superhump phases. Because WZ Sge-type superoutbursts are essentially different from SU UMa-type ones, WZ Sge-type DNe are defined by the presence of the early superhump phase according to the modern criteria (Kato, 2015). For these reasons, WZ Sge-type superoutbursts are brighter and longer than SU UMa-type ones.

As indicated in Levitan et al. (2015), many AM CVn stars could show WZ Sge-type superoutbursts since they have low $q$ and low mass-transfer rate, especially in long period systems. Actually, some objects have shown WZ Sge-like light curves. However, the reliable evidence of WZ Sge-type superoutbursts, namely the early superhump phase, has never been observed in AM CVn stars and candidates. Because we can estimate $P_{\rm orb}$ from the early superhump period, WZ Sge-type superoutbursts are not just large and rare superoutbursts but the important messengers of the binary parameters. Furthermore, we can also estimate the mass ratios from intensive time-series observations of WZ Sge-type superoutbursts and evaluate the evolutionary path as will be discussed in section 5.3.

In this paper, we report on our time-series observations of the 2015 and 2017 outbursts of the AM CVn candidate NSV 1440. Although there is no spectroscopic confirmation, the short period superhump and outburst behavior suggest that the object is an AM CVn star. Actually, the object is often treated as an AM CVn star, e.g. Ramsay et al. (2018). The object showed the first WZ Sge-type superoutbursts in AM CVn stars and candidates. This fact implies that we can understand outbursts in AM CVn stars by analogy with hydrogen-rich DNe.

2 NSV 1440

NSV 1440 was a variable star candidate listed in the New Catalogue of Suspected Variable Stars (NSV, Kukarkin et al. (1982)) with the brightness range from 12.6 up to 15.0 mag. The object is also known by the names BV 1025, ASASSN-15sz and GALEX J035517.7-822612. The coordinates of the object are RA = 03:55:17.83 and Dec = -82:26:11.5 at J2000. The quiescent magnitudes in Gaia Data Release 2 are $G=18.5126(72)$, $BP=18.4139(331)$ and $RP=18.4239(684)$ (Gaia Collaboration et al., 2016, 2018; Riello et al., 2018). By using these values and table A.2 in Evans et al. (2018), we can estimate the quiescent $V$ mag of 18.53(5). The object has a GALEX counterpart with near-UV (NUV) and far-UV (FUV) magnitudes of 18.305(57) and 18.286(96) (Martin et al., 2005). Two historical outbursts were recorded in the All Sky Automated Survey-3 (ASAS-3, Pojmański (2002)), cf. the light curve of ASAS-3 in figure E2. The 2003 outburst was detected at 13.544 mag on BJD 2452929.740037, and the 2005 one was detected at 13.492 mag on BJD 2453669.797309.

The 2015 outburst was detected at $V=$ 13.8 on November 20 (BJD 2457339.62) by the All-Sky Automated Survey for Supernovae (ASAS-SN) (Shappee et al., 2014). The 2017 outburst was detected at a visual magnitude of 13.0 on August 21 (BJD 2457987.27) by R. Stubbings (vsnet-alert 21352111 VSNET-alert archive is available at

¡http://ooruri.kusastro.kyoto-u.ac.jp/pipermail/vsnet-alert/¿ ). After these detections, we performed the observation campaigns.

3 Observation and Analysis

Our time-series observations are summarized in table E1 and E2222 Figure E1–E2 and tables E1–E4 are available online as the supplementary data for this article. . The typical exposure time is 30–120 sec. The data were acquired by time-series unfiltered CCD photometry using 30–40 cm class telescopes by the VSNET Collaboration (Kato et al., 2004). The times of the observations were corrected to Barycentric Julian Date (BJD). We adjusted the zero-point of each observer to the data of Franz-Josef Hambsch.

We used the phase dispersion minimization (PDM) method for analyzing the superhump periods. We estimated $1\sigma$ errors by using the methods in Fernie (1989) and Kato et al. (2010). Before our period analyses, we subtracted the global trend of the light curve which was calculated using locally-weighted polynomial regression (LOWESS, Cleveland (1979)). We used $O-C$ diagrams which are sensitive to subtle variations of the superhump period. The times of superhump maxima, which are used to draw the $O-C$ diagrams and are listed in table E3 and E422footnotemark: 2, were determined by the same method as described in Kato et al. (2009). The number in the parentheses after each value represents $1\sigma$ error, e.g. $0.12(3)$ means $0.12\pm 0.03$.

4 Result

4.1 Overall Light Curve

Figure 1 shows the overall light curves of the 2015 and 2017 outbursts. We also added the $V$ and $g$-band data obtained by the ASAS-SN Sky Patrol (Shappee et al., 2014; Kochanek et al., 2017). We should note that the ASAS-SN data around 16.5 mag might include systematic errors due to their limiting magnitudes. The horizontal axis “Date” of the 2015 and 2017 outbursts are defined to be BJD $-$ 2457346.751 and BJD $-$ 2457982.000, respectively. Each light curve shows two superoutbursts (double superoutburst) and rebrightenings. We respectively marked the superoutbursts, rebrightenings and “small rebrightenings” with the labels “SO”, “R” and “r”. The overall light curves are roughly consistent with each other.

According to the 2015 light curve, the maximum brightness value of the first superoutburst (SO1) is V=12.85 on Date $=$ 0.85. The SO1 lasted for about 4 d and the object rapidly faded to 18.0 mag. Then the object brightened again and reached the maximum of the second superoutburst (SO2) on Date $=$ 7.6. The duration of the SO2 is about 5 d. Unfortunately, there is no data of the plateau of the SO1 in 2017 due to the observational gap, hence we cannot exclude the possibility that the SO1 in 2017 is not a superoutburst but a precursor outburst. After the end of the SO2, the object showed a slow decline with multiple rebrightenings. In 2017, the object returned to the quiescent magnitude of V $=$ 18.53 around Date $=$ 120.

4.2 Early superhumps

During the SO1, we succeeded in detecting double-wave modulations with a constant period of 0.0252329(49) d. The result of the period analysis and the averaged profile are shown in the left panels of figure 2. Because the SO1 is brighter than the SO2 which shows the ordinary superhumps, the disk should expand beyond the 3:1 resonance radius and reach the 2:1 one. As explained in introduction, the 2:1 resonance suppresses the 3:1 resonance (Lubow, 1991a; Osaki, Meyer, 2003). If the disk did not reach the 2:1 resonance radius, the object should show ordinary superhumps during the SO1. As explained in next section, the growing ordinary superhumps were detected in the rising part of the SO2, thus we propose that the modulations in the SO1 are early superhumps.

The constant period and the characteristic double-wave profile also suggest that they are early superhumps. Thus, we can use the period of the early superhump as $P_{\rm orb}$.

4.3 Ordinary superhumps

After the end of the SO1, ordinary superhumps began to grow. We drew the $O-C$ diagrams of superhump maxima (figure 3). For the classification and the interpretation of the superhump stages, see Kato et al. (2009) and Kato, Osaki (2013). In WZ Sge-type DNe, “late-stage superhumps” are usually observed instead of stage C ones after the main superoutburst (Kato, 2015). $P_{\rm SH}$ in the late stage is shorter than in stage A but longer than in stage B.

We can distinguish between stage A, B and late-stage superhumps from the $O-C$ diagrams. Around the rapid fading from the SO1 (marked “F” in figure 3), the object showed short-period modulations (hereafter we call this term “fading stage”). We will discuss the modulations in the fading stage in section 5.2. We summarized the estimated periods and the Dates used for our analysis in table 1. The periods in 2017 have significantly larger errors due to the lacking data, thus we will basically use the values in 2015. The right panel of figure 2 shows phase-averaged profiles in 2015.

4.4 Rebrightenings

Each light curve shows eight rebrightenings. The timings of the rebrightenings are almost the same except for the last one. The duration and the amplitudes are 1.5 d and 2.1–2.6 mag, respectively. Only in the 2015 outburst, the object showed two “short rebrightenings” whose duration and amplitudes are respectively $\sim$ 0.6 d and $\sim$ 1 mag (you can see the enlarged light curve of the rebrightenings in figure E122footnotemark: 2).

We extracted the linear rising/fading part of the rebrightenings in 2015 and evaluated the rising/fading rates. The averaged rising/fading rates in the normal rebrightenings are approximately -15(2) mag/d and 2.2(2) mag/d, respectively. Such a rapid rising suggests that the normal rebrightenings are outside-in outbursts. In contrast, the rising/fading rates in the short rebrightenings are about -6 mag/d and 4.7 mag/d, respectively. The slow rising implies that the short rebrightenings are inside-out outbursts and arose only in the inner part of the disk.

5 Discussion

5.1 WZ Sge-type superoutburst

As mentioned in the introduction, many AM CVn stars have low $q$ and can potentially cause a WZ Sge-type superoutburst. A part of H-rich CVs with extreme low $q<0.06$ show double superoutbursts which are composed of the first superoutburst with early superhumps and the second superoutburst with ordinary superhumps (Kato, 2015). Because the growth time of the 3:1 resonance is proportional to $q^{2}$ (Lubow, 1991a), the systems having low $q$ cannot maintain the superoutburst just after the disappears of the early superhumps. When the ordinary superhump sufficiently develops, the object undergoes the second superoutburst (Kimura et al., 2016). The outburst behaviors of NSV 1440 are in agreement with this interpretation. Although we don’t know the true $P_{\rm orb}$ of NSV 1440, we can interpret the modulations in the SO1 as early superhumps on the basis of the outburst morphology. Thus NSV 1440 is the first promising WZ Sge-type DN in AM CVn stars and candidates.

WZ Sge-type superoutbursts in AM CVn stars could be double superoutbursts because of their extreme low $q$. Levitan et al. (2015) investigated the long-term light curves of many AM CVn stars and confirmed WZ Sge-type DNe-like light curves. The light curve of SDSS J172102.48+273301.2 resembles those of NSV 1440 closely (figure 10 in Levitan et al. (2015)). There is however no time-resolved data and we cannot confirm the presence of early superhumps. SDSS J090221.35+381941.9 reported in Kato et al. (2014) showed a precursor outburst one week before the SU UMa-type superoutburst. The precursor may have been a superoutburst with early superhumps, but they missed the overall profile of the precursor. Recently, SDSS J141118.31+481257.6 and ASASSN-18rg also showed double superoutburst-like phenomena (Isogai et al. in preparation).

5.2 Orbital-period modulations in the fading stage

The periods of the modulations in the fading stage are close to $P_{\rm orb}$ (table 1). GW Lib, a typical H-rich WZ Sge-type DN, also showed such orbital-period modulations in the fading stage (see figure 33 in Kato et al. (2009)). It is known that the pressure effect in the disk shortens $P_{\rm SH}$ (Lubow, 1992). If the pressure effect is amplified in the fading stage, $P_{\rm SH}$ might match with $P_{\rm orb}$. The right panel of figure 2 shows the orbital-period modulations have a sine wave shape. The period and the profile may give us the impression that the bright spot was brightened in the fading stage, namely the mass transfer was enhanced. However, it is difficult to understand the reason why such orbital modulations become visible only in the fading stage.

5.3 Mass ratio and evolutionary channel

Three evolutionary channels (WD, helium-star and evolved-CV channels) have been proposed to form AM CVn stars, but the contribution of each channel is poorly understood. The secondaries of WD channel systems are fully-degenerate WDs. Whereas, those of helium-star and evolved-CV channel systems are initially semi-degenerate stars and gradually evolve into fully-degenerate ones (cf. Deloye et al. (2007)). Thus, secondary masses help to reveal their evolutionary channels.

We can also use mass ratio $q$, which is easier to obtain than donor mass.

The empirical relation between $q$, $P_{\rm orb}$ and $P_{\rm SH}$ of hydrogen-rich DNe has been widely known, e.g. Patterson et al. (2005). However, Roelofs et al. (2006b) confirmed that $q$ from the empirical law is significantly different from their spectroscopic measurement. Furthermore, Pearson (2007) indicated that superhump periods are affected by the pressure effect in the disk and computed the pressure effect of AM CVn stars. According to his formulation, the pressure effect also depends on the mass-radius relation of the secondary. Because the mass-radius relation of AM CVn stars differs with the evolutionary scenarios, Pearson (2007) concluded that we should not use the empirical law for AM CVn stars. Osaki, Kato (2013) interpreted that $P_{\rm SH}$ of the growing (stage A) superhump corresponds to the dynamical precession rate at the 3:1 resonance radius based on the Kepler’s complete light curve. Kato, Osaki (2013) investigated $P_{\rm SH}$ and $q$ of hydrogen-rich CVs and have established the $q$ estimation method in a purely dynamical way. They confirmed that $q$ from stage A are in good agreement with $q$ from the eclipse measurement. Because this method does not depend on the disk composition and the secondary mass-radius relation, we can apply to other DN cousins. In fact, Ohnishi et al. (submitted) estimated $q$ of the metal-poor (population II) system OV Boo by using $P_{\rm SH}$ in stage A and the early superhump period which is regarded as $P_{\rm orb}$. They succeeded in confirming that $q$ from the stage A method is consistent with $q$ from the eclipse measurement. The metal abundance significantly affects the mass-radius relation (Stehle et al., 1997) and the viscosity in the disk (Pojmanski, 1986). Therefore, this result strongly suggests that we can also apply the stage A method to AM CVn stars. However, we need to confirm the orbital period and mass ratio via spectroscopies or eclipse observations.

Kato, Osaki (2013) proposed that $q$ can be estimated by using the fractional superhump excess $\varepsilon^{*}\equiv 1-P_{\rm orb}/P_{\rm SH}$ in stage A. On the basis of the theoretical equations in Kato, Osaki (2013) and $\varepsilon^{*}=0.0174(8)$, we obtained $q=0.045(2)$.

Armstrong et al. (2012) derived the following evolutionary tracks from the Kepler’s third law, the secondary’s Roche lobe-filling condition (Faulkner et al., 1972), the mass-radius relation of fully-degenerate stars (Zapolsky, Salpeter, 1969) and that of semi-degenerate stars (Savonije et al., 1986):

[TABLE]

[TABLE]

Figure 4 shows the above evolutionary tracks on the $P_{\rm orb}$-$q$ plane. The dashed and solid curves respectively mean semi and fully-degenerate secondaries assuming $M_{1}$. The value of NSV 1440 suggests that the object has a semi-degenerate secondary, and hence the object is an AM CVn star in a helium-star or evolved-CV channel.

5.4 Period variations of superhumps

From the $O-C$ diagrams, we estimated the period derivative $P_{\rm dot}=\dot{P}/P$ of stage B to be $-1.4(5)\times 10^{-5}$ in 2015 and $-1.5(7)\times 10^{-5}$ in 2017. In hydrogen-rich CVs, it is empirically known that the $P_{\rm dot}$ depends on $P_{\rm orb}$ and $q$. Especially, $P_{\rm dot}$ of WZ Sge-type DNe have good correlation with $q$. Kato (2015) derived the empirical relation $q=0.0043(9)P_{\rm dot}\times 10^{5}+0.060(5)$ for H-rich WZ Sge-type DNe. Then, we obtained $q=$ 0.054(6) in 2015 and 0.053(6) in 2017 which are larger than $q=0.045(2)$ estimated in section 5.3. We should modify the relation for AM CVn stars.

The pressure effect in the disks in He-rich CVs appears to be larger than that in H-rich CVs because of the higher ionization temperature (Pearson, 2007). Kato et al. (2014) argued that the period variation between stage A and B reflects the pressure effect. For this purpose, we calculated $\varepsilon^{*}({\rm stage\ A})-\varepsilon^{*}({\rm stage\ B})=0.0125(8)$. This value is in agreement with those in H-rich CVs of 0.010-0.015 (Kato et al., 2009) against the expectation. The reason may be that the pressure effect also depends on other parameters, e.g. $q$ (see equation 24 in Pearson (2007)).

5.5 Supercycle

As mentioned in section 2, the four outbursts have been detected: $V=13.544$ in 2003, $V=13.492$ in 2005, $V=13.8$ in 2015, $V=13.0$ in 2017. The complete light curves of ASAS-3 and ASAS-SN are shown in figure E2. Although there is no time-resolved data in 2003 and 2005, their outburst maxima suggest that they are superoutbursts. As you can see in figure 1, all superoutbursts are brighter than 14.0 mag, and all rebrightenings (normal outbursts) are fainter than 14.0 mag. These superoutburst intervals implies the supercycle of two years. If this inference is correct, we can calculate the averaged supercycle of 728(7) d. Levitan et al. (2015) empirically obtained the following relation between the outburst recurrence time $\Delta T$ and $P_{\rm orb}$:

[TABLE]

This equation suggests that the supercycle of NSV 1440 is 474.6 d. This value is roughly consistent with our estimation. However, there is some uncertainty. Although ASAS-3 had observed around NSV 1440 for nine years, the detected outburst is only two. It might be caused by the shallow limiting magnitude of $V\sim 14$ (Pojmanski, 2004) and/or some observation gaps. We should correct the supercycle by further observations.

6 Summary

The outbursts of NSV 1440 showed the following features, are known in H-rich WZ Sge-type DNe: (1) double superoutbursts; (2) early superhumps; (3) late-stage superhumps instead of stage C ones; (4) orbital-period modulations in the fading stage; (5) multiple rebrightenings. Therefore, we interpreted NSV 1440 as the first WZ Sge-type DN in AM CVn stars and candidates. This discovery implies that many AM CVn stars also show WZ Sge-type superoutbursts. We should note that early and ordinary superhumps in WZ Sge-type superoutburst tell us the basic binary parameters (i.e., orbital period and mass ratio).

We obtained the early superhump period of 0.0252329(49) and the stage A superhump one of 0.025679(20) d from the 2015 outburst. On the basis of these periods and the method of Kato, Osaki (2013), we estimated $q=0.045(2)$. This value suggests that the object is an AM CVn star and has a semi-degenerate secondary. In other words, the object can be a helium-star or evolved-CV channel system. However, we should note that the validity of the $q$ estimation method from stage A $P_{\rm SH}$ is not confirmed in AM CVn stars. Therefore, we need to compare $q$ from stage A with $q$ from other methods also in AM CVn stars.

Supplementary Material

The following supplementary data is available in the online article. figure E1–E2 and tables E1–E4.

Acknowledgments

This work was supported by the Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows (No. 17J10039). This work was also partially supported by the Grant-in-Aid “Initiative for High-Dimensional Data-Driven Science through Deepening of Sparse Modeling” (25120007) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We are also thankful to the AAVSO International Database contributed by many worldwide observers and to the survey project ASAS-SN. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.