The Extended IRTF Spectral Library: Expanded coverage in metallicity, temperature, and surface gravity

TL;DR

This paper introduces an expanded infrared spectral library of 284 stars covering a broad range of metallicities, temperatures, and gravities, with a spectral interpolator for modeling stellar spectra based on these parameters.

Contribution

The paper provides a new, extensive spectral library with improved metallicity coverage and a data-driven spectral interpolator, enhancing stellar characterization across diverse stellar types.

Findings

Spectral library covers $0.7-2.5\,\mu m$ with 284 stars.

Library extends metallicity range to $-1.7 < [Fe/H] < 0.6$.

Spectral interpolator models spectra as a function of stellar parameters.

Abstract

We present a $0.7-2.5\mu m$ spectral library of 284 stars observed with the medium-resolution infrared spectrograph, SpeX, at the 3.0 meter NASA Infrared Telescope Facility (IRTF) on Maunakea, Hawaii. This library extends the metallicity range of the IRTF Cool Star library beyond solar metallicity to $-1.7 <$ [Fe/H] $< 0.6$. All of the observed stars are also in the MILES optical stellar library, providing continuous spectral coverage for each star from $0.35-2.5\mu m$. The spectra are absolute flux calibrated using Two Micron All Sky Survey photometry and the continuum shape of the spectra is preserved during the data reduction process. Synthesized $JHK_S$ colors agree with observed colors at the $1-2\%$ level, on average. We also present a spectral interpolator that uses the library to create a data-driven model of spectra as a function of $teff$, $logg$, and [Fe/H]. We use the library and interpolator to compare empirical trends with theoretical predictions of spectral feature behavior as a function of stellar parameters. These comparisons extend to the previously difficult to access low-metallicity and cool dwarf regimes, as well as the previously poorly sampled super-solar metallicity regime. The library and interpolator are publicly available.

Tables

Table 1. Table 1 Valid ranges for SPI interpolation

	Training			Interpolating
Regime	$T_{\mathrm{eff}}$	log$g$	[Fe/H]	$T_{\mathrm{eff}}$	log$g$	[Fe/H]
Cool Dwarfs	1100-5500	3.5-6.5	-2.5-0.6	2500-4000	-0.5-3.5	-2.0-0.6
Cool Giants	1100-4500	-1.0-2.75	-2.5-0.6	2500-4000	$>$3.5	-2.0-0.6
Warm Dwarfs	3000-6500	3.0-5.75	-2.5-0.6	4000-6000	-0.5-3.5	-2.0-0.6
Warm Giants	3500-6500	-0.75-4.0	-2.5-0.6	4000-6000	$>$3.5	-2.0-0.6
Hot Stars	5500-12,500	2.5-5.5	-2.5-0.6	6000-12,000	5.0	-2.0-0.6

Table 2. Table 2 The library stars.

Name	MILES	Standard		RA				DEC		[Fe/H]	KS	E(B-V)	Velocity	log Lbol	Q1	P2	S3
	ID	Star	hh	mm	ss	$+/-$	dd	mm	ss		(mag)	(mag)	(km $s^{-1}$)	(L⊙)	Flag	Flag	Flag
HD225239	0003F	HD007215-A0V	00	04	53.7603	+	34	39	35.259	-0.51	4.44	0.050	-48.2	0.75	0	0	1
HD000448	0009F	CCDM J00209+1059AB-A0V	00	09	02.4241	+	18	12	43.066	0.02	3.32	0.025	-15.9	1.55	0	1	0
BD+130013	0010F	HD007215-A0V	00	12	30.3109	+	14	33	48.678	-0.75	6.24	0.011	-24.0	-0.15	0	0	0
HD001326B	0012F	HD001561-A0Vs	00	18	25.498	+	44	01	37.64	-0.57	5.95	0.001	-7.3	-2.45	1	0	0
HD001461	0013F	HD013936-A0V	00	18	41.8672	-	08	03	10.802	0.19	4.9	0.044	-37.7	0.08	0	0	0
HD001918	0014F	HD001561-A0Vs	00	23	43.2412	+	45	05	20.892	-0.4	5.23	0.037	59.5	2.05	0	0	0
HD003567	0022F	HD001154-A0V	00	38	31.9474	-	08	18	33.395	-1.14	7.89	0.000	-41.4	0.22	0	0	0
HD003546	0023F	HD006457-A0Vn	00	38	33.3461	+	29	18	42.313	-0.66	2.07	0.000	-58.0	1.68	0	0	0
HD003574	0024F	HD001561-A0Vs	00	39	09.8946	+	49	21	16.521	0.01	1.6	0.048	-13.9	3.82	0	0	0
HD004307	0028F	HD015130-A0V	00	45	28.6878	-	12	52	50.914	-0.24	4.62	0.000	-25.2	0.44	0	0	0
HD004744	0033F	HD006457-A0Vn	00	49	52.7904	+	30	27	01.028	-0.74	4.93	0.010	-148.3	1.61	0	0	0
HD004906	0034F	HD006229-G5III	00	51	14.0528	+	18	47	25.153	-0.66	6.77	0.028	-127.4	0.65	0	0	0
NGC288-77	0897C	HD004329-A0V	00	52	43.00	-	26	27	28.0	-1.32	10.01	0.030	-31.8	2.85	0	0	0
HD005384	0036F	HD013936-A0V	00	55	42.3993	-	07	20	49.742	0.18	2.42	0.012	-49.1	2.5	1	0	0
HD005780	0038F	CCDM J00209+1059AB-A0V	00	59	23.3126	+	00	46	43.563	-0.71	4.22	0.000	-90.0	2.41	0	0	1
HD006229	0043F	HD006457-A0Vn	01	03	36.4553	+	23	46	06.377	-1.14	6.57	0.000	-103.5	1.51	0	0	1
HD006497	0045F	HD223386-A0V	01	07	00.1738	+	56	56	05.904	0.04	3.88	0.014	-75.5	1.42	0	0	0
HD006834	0049F	HD007215-A0V	01	09	35.2623	+	39	46	51.765	-0.58	7.29	0.005	7.8	0.38	0	0	1
HD006755	0050F	HD223386-A0V	01	09	43.0646	+	61	32	50.190	-1.58	5.66	0.060	-286.6	1.19	0	0	0
HD006833	0051F	HD001561-A0Vs	01	09	52.2648	+	54	44	20.278	-0.84	4.04	0.047	-241.6	1.95	0	0	1
HD007106	0052F	HD007215-A0V	01	11	39.6364	+	30	05	22.690	-0.02	2.15	0.011	19.1	1.59	0	0	0
HD007351	0053F	HD007215-A0V	01	14	04.9061	+	28	31	46.471	-0.35	1.64	0.048	-8.7	3.32	0	0	0
HD007672	0056F	CCDM J00209+1059AB-A0V	01	16	36.2886	-	02	30	01.321	-0.42	3.38	0.076	23.7	1.55	0	1	0
HD008724	0057F	HD006457-A0Vn	01	26	17.5949	+	17	07	35.127	-1.63	5.64	0.020	-112.8	1.97	0	1	0
HD009919	0064F	HD006457-A0Vn	01	37	05.9152	+	12	08	29.518	-0.35	4.58	0.006	38.4	0.72	0	0	0
HD010700	0067F	HD013936-A0V	01	44	04.0833	-	15	56	14.926	-0.46	1.79	0.004	-23.4	-0.32	1	0	1
HD011397	0072F	HD021875-A0V	01	51	40.5274	-	16	19	03.526	-0.58	7.27	0.070	2.7	-0.16	0	0	0
BD+290366	0077F	BD+320409-A0V	02	10	24.5278	+	29	48	23.669	-0.95	7.22	0.00	45.0	-0.1	0	0	0
HD013520	0080F	HD013869-A0V	02	13	13.3238	+	44	13	53.954	-0.27	1.33	0.020	-46.7	2.77	0	0	0
BD-010306	0081F	HD018571-A0V	02	14	40.2986	-	01	12	05.119	-0.89	7.52	0.000	18.0	-0.11	0	0	0
HD013783	0082F	HD012468-A0V	02	16	49.2129	+	64	57	09.380	-0.49	6.59	0.000	-31.8	-0.21	0	0	0
HD014802	0084F	HD017224-A0V	02	22	32.5464	-	23	48	58.779	-0.07	3.74	0.000	-14.2	0.47	0	1	0
HD016673	0092F	HD015130-A0V	02	40	12.4215	-	09	27	10.361	0.0	4.53	0.005	-10.2	0.26	0	0	1
HD017361	0098F	HD013869-A0V	02	47	54.5414	+	29	14	49.613	0.02	2.1	0.020	-18.9	1.6	0	0	0
HD017491	0099F	HD013936-A0V	02	47	55.9222	-	12	27	38.322	-0.15	0.36	0.034	-11.7	3.33	0	0	0
HD017548	0101F	HD021686-A0Vn	02	48	51.8520	-	01	30	34.747	-0.53	6.76	0.008	-35.5	0.13	0	0	0
HD018191	0103F	HD016811-A0V	02	55	48.4980	+	18	19	53.902	-0.05	-0.87	0.164	81.8	3.15	0	0	0
HD019373	0108F	HD021038-A0V	03	09	04.0198	+	49	36	47.799	0.11	2.72	0.034	56.3	0.29	0	0	0
HD020893	0114F	HD023258-A0V	03	22	45.2400	+	20	44	31.438	0.07	2.19	0.031	-21.6	2.08	0	0	0
BD+430699	0115F	HD021038-A0V	03	23	33.4875	+	43	57	26.222	-0.38	6.54	0.007	6.6	-0.69	0	0	0
HD021017	0116F	HD023258-A0V	03	24	18.4745	+	24	43	26.617	0.07	2.89	0.004	-24.5	1.45	1	0	0
HD021197	0117F	HD025175-A0V	03	24	59.7314	-	05	21	49.523	0.13	5.12	0.072	-36.8	-0.6	0	0	1
HD021581	0118F	HD018571-A0V	03	28	54.486	-	00	25	03.11	-1.51	6.41	0.000	100.5	1.35	0	0	0
HD022879	0123F	HD031295-A3Va	03	40	22.0641	-	03	13	01.124	-0.8	5.18	0.000	118.6	0.05	0	0	0
HD023439A	0127F	HD021038-A0V	03	47	02.113	+	41	25	38.06	-0.9	6.12	0.010	34.5	-1.0	0	0	0
HD023439B	0128F	HD021038-A0V	03	47	02.636	+	41	25	42.56	-1.09	6.35	0.010	27.3	-1.0	0	0	0
HD023841	0130F	HD021686-A0Vn	03	48	30.7665	+	09	38	45.410	-0.66	3.8	0.053	-94.1	2.42	0	0	1
HD024341	0133F	HD029526-A0V	03	54	51.1901	+	52	25	11.526	-0.62	6.11	0.023	99.2	0.3	0	0	0
HD024421	0134F	HD029526-A0V	03	55	37.0801	+	52	13	36.550	-0.29	5.47	0.003	-56.4	0.32	0	0	0
HD025673	0138F	HD021875-A0V	04	04	20.3036	-	04	39	18.471	-0.4	7.46	0.006	81.3	-0.48	0	0	0
HD026297	0139F	HD021875-A0V	04	09	03.4176	-	15	53	27.063	-1.79	4.63	0.017	25.1	2.73	0	0	0
HD284248	0143F	HD023258-A0V	04	14	35.5155	+	22	21	04.261	-1.55	7.87	0.000	303.3	0.09	0	0	0
BD-060855	0144F	HD025792-A0V	04	14	58.1083	-	05	37	48.856	-0.69	8.79	0.01	324.8	-0.54	0	0	0
HD027126	0147F	HD025152-A0V	04	18	29.5492	+	35	59	30.080	-0.38	6.64	0.000	-56.5	-0.09	0	0	1
HD027371	0149F	HD032358-B6V	04	19	47.6038	+	15	37	39.515	0.15	1.52	0.014	65.2	1.94	0	0	0
HD027771	0150F	HD025175-A0V	04	23	32.3310	+	14	40	13.717	0.27	7.14	0.000	20.1	-0.33	0	0	0
HD285773	0153F	HD025175-A0V	04	29	31.6067	+	17	53	35.466	0.25	7.05	0.000	9.8	-0.37	0	0	0
BD+501021	0158F	HD029526-A0V	04	38	07.8341	+	51	10	12.467	-0.65	8.28	0.060	-31.8	-0.55	0	0	0
HD030649	0162F	HD031069-A0V	04	51	43.5572	+	45	50	02.971	-0.48	5.44	0.000	20.0	0.08	0	0	0
HD031128	0163F	HD034868-A0V	04	52	09.9101	-	27	03	50.950	-1.45	7.74	0.000	85.1	-0.11	0	0	0
HD031295	0166F	HD031411-A0V	04	54	53.7287	+	10	09	02.995	-0.73	4.42	0.100	-17.0	1.15	0	1	0
HD031767	0167F	HD034317-A0V	04	58	32.9021	+	01	42	50.458	-0.02	1.34	0.101	4.4	3.36	0	0	0
HD033608	0173F	HD031411-A0V	05	11	19.1768	-	02	29	26.817	0.21	4.82	0.000	62.2	0.62	0	0	0
HD034411	0176F	HD031069-A0V	05	19	08.4742	+	40	05	56.582	0.08	3.04	0.000	32.8	0.27	0	0	0
HD035179	0178F	HD035505-A0V	05	22	21.0066	-	14	23	50.061	-0.6	7.1	0.000	13.7	1.96	0	0	0
M79_153	0915C	HD040972-A0V	05	24	09.1300	-	24	34	16.1000	-1.6	9.61	0.010	-19.9	-1.0	0	0	1
M79_160	0916C	HD040972-A0V	05	24	09.4000	-	24	33	29.9000	-1.6	10.26	0.010	216.4	3.06	0	0	0
M79_223	0917C	HD040972-A0V	05	24	18.4860	-	24	31	43.3800	-1.6	9.83	0.010	188.7	3.19	0	0	0
HD035296	0180F	HD035036-A0V	05	24	25.4638	+	17	23	00.716	0.01	4.04	0.000	78.5	0.1	0	0	1
HD035620	0181F	HD035036-A0V	05	27	38.8860	+	34	28	33.212	0.1	2.1	0.115	52.2	2.48	0	1	0
HD036003	0182F	HD037887-B9.5V	05	28	26.0960	-	03	29	58.399	-0.15	4.88	0.011	-19.9	-0.71	0	0	0
HD036395	0183F	HD037887-A0V	05	31	27.3959	-	03	40	38.031	-0.05	4.04	0.006	-24.3	-1.27	0	0	0
HD037160	0184F	HD035656-B9V	05	36	54.3881	+	09	17	26.409	-0.64	1.81	0.000	124.2	1.47	0	0	0
HD037828	0187F	HD035505-A0V	05	40	54.6451	-	11	12	00.191	-1.41	4.06	0.020	188.5	2.55	0	0	0
HD037984	0189F	HD034317-A0V	05	42	28.6327	+	01	28	28.665	-0.52	2.21	0.010	80.4	2.02	0	0	0
HD038393	0191F	* 10 lep-A0V	05	44	27.7908	-	22	26	54.180	-0.09	2.51	0.000	-17.8	0.28	0	0	0
HD039364	0196F	* 10 Lep-A0V	05	51	19.2961	-	20	52	44.723	-0.74	1.4	0.000	81.9	1.54	0	0	0
HD039833	0198F	HD039953-A0V	05	55	01.958	-	00	30	28.69	0.18	6.15	0.010	6.8	0.08	0	0	0
HD041312	0203F	HD042729-A0V	06	03	15.6045	-	26	17	04.355	-0.75	1.69	0.030	149.4	2.43	1	0	0
HD042543	0211F	HD046553-A0Vnn	06	12	19.0986	+	22	54	30.642	0.18	0.81	0.606	51.6	5.19	0	0	0
HD043380	0215F	HD045105-A0V	06	18	16.8650	+	46	21	37.593	-0.05	3.65	0.019	-27.5	1.74	1	0	0
HD044007	0216F	HD038206-A0V	06	18	48.5271	-	14	50	43.425	-1.53	5.7	0.000	162.1	1.3	0	0	1
HD044030	0219F	HD046553-A0Vnn	06	20	35.3327	+	25	36	29.306	-0.51	4.14	0.107	-132.7	2.65	0	0	0
HD045282	0222F	HD045137-A0V	06	26	40.7734	+	03	25	29.794	-1.42	6.09	0.000	281.2	1.11	0	0	0
HD045829	0223F	HD043583-A0V	06	30	02.2945	+	07	55	16.009	0.11	3.35	0.228	58.3	4.06	0	0	0
HD047914	0227F	HD045105-A0V	06	43	04.9710	+	44	31	28.022	0.04	1.71	0.033	-43.7	2.2	1	0	0
HD048682	0232F	HD045105-A0V	06	46	44.3381	+	43	34	38.726	0.11	4.13	0.000	-1.0	0.13	0	1	0
HD054719	0245F	HD058296-A0V	07	11	08.3704	+	30	14	42.583	0.13	1.68	0.020	-2.6	2.3	0	0	0
HD055496	0246F	HD056341-A0V	07	12	11.3771	-	22	59	00.619	-1.48	5.93	0.020	305.7	2.15	0	0	0
HD056274	0249F	HD067725-B8V	07	15	50.7956	-	13	02	58.131	-0.53	6.2	0.079	80.9	-0.07	0	0	1
HD058551	0255F	HD064648-A0Vs	07	26	50.2521	+	21	32	08.320	-0.42	5.24	0.000	14.3	0.25	0	0	0
HD059374	0257F	CCDM J07274+1519AB-A0V	07	30	29.0172	+	18	57	40.620	-0.82	6.98	0.000	75.7	-0.05	0	0	1
HD059984	0259F	HD067725-B8V	07	32	05.7628	-	08	52	52.776	-0.68	4.48	0.023	14.9	0.37	0	1	0
BD-011792	0266F	HD079107-A0V	07	39	50.1104	-	01	31	20.372	-0.81	7.04	0.000	56.8	0.89	0	0	0
HD061935	0270F	HD056525-A0V	07	41	14.8325	-	09	33	04.071	-0.06	1.64	0.015	16.9	1.74	0	0	0
BD+002058A	0272F	HD079108-A0V	07	43	43.9549	-	00	04	00.899	-1.22	8.84	0.02	-54.4	-0.07	0	0	0
BD-182065	0278F	HD067213-A0V	07	52	38.0071	-	18	35	37.734	-0.71	7.27	0.000	111.3	-1.0	0	0	0
HD063791	0281F	HD237611-A0V	07	54	28.7238	+	62	08	10.761	-1.62	5.43	0.03	-128.8	2.89	0	0	1
HD065583	0285F	HD064648-A0Vs	08	00	32.1289	+	29	12	44.471	-0.65	5.09	0.000	-10.8	-0.34	0	0	0
HD073898	0307F	HD079290-A0V	08	39	42.4741	-	29	33	39.898	-0.56	2.9	0.043	1.2	1.75	0	0	1
HD073394	0309F	HD063586-A0Vn	08	40	22.5437	+	51	45	06.558	-1.49	4.96	0.002	-80.2	2.34	0	0	0
HD074011	0312F	HD071906-A0V	08	42	30.8192	+	34	11	15.699	-0.56	5.79	0.006	83.0	0.31	0	0	0
HD074377	0316F	HD071906-A0V	08	45	10.3977	+	41	40	18.615	-0.37	6.13	0.002	-9.2	-0.5	0	0	0
HD074721	0317F	HD075137-A0V	08	45	59.2615	+	13	15	48.607	-1.32	8.52	0.032	75.7	2.84	0	0	0
HD074462	0319F	* 39 UMa-A0III	08	48	20.6521	+	67	26	59.893	-1.4	6.05	0.020	-206.7	2.05	0	0	0
HD075318	0320F	HD079108-A0V	08	49	21.2072	+	03	41	02.392	-0.13	6.08	0.000	64.0	-0.12	0	0	0
HD075691	0321F	* eta pyx-A0V	08	50	31.9228	-	27	42	35.442	-0.16	1.14	0.033	15.0	2.11	0	0	0
HD076151	0323F	HD073687-A0V	08	54	17.9480	-	05	26	04.058	0.15	4.46	0.000	46.6	0.0	0	0	0
HD076932	0325F	HD073687-A0V	08	58	43.9331	-	16	07	57.813	-0.82	4.36	0.000	91.2	0.21	0	0	0
HD076813	0330F	HD071906-A0V	08	59	32.6543	+	32	25	06.809	-0.06	3.15	0.331	4.1	2.02	0	1	0
HD077338	0331F	HD073495-A0V	09	01	12.4941	-	25	31	37.426	0.36	6.76	0.029	8.3	-0.31	0	1	0
HD077236	0332F	HD079108-A0V	09	01	14.7956	-	02	33	41.689	-0.89	4.64	0.000	144.3	1.98	0	0	0
HD078737	0337F	HD073495-A0V	09	09	03.3696	-	27	01	49.314	-0.46	7.74	0.005	1.5	0.65	0	1	0
HD081029	0345F	HD079108-A0V	09	23	15.7647	+	03	30	04.997	-0.08	6.49	0.065	60.8	1.03	0	1	0
HD081797	0347F	HD084886-A0V	09	27	35.2427	-	08	39	30.958	0.01	-1.13	0.012	0.3	2.89	1	0	0
HD082074	0349F	HD079108-A0V	09	29	32.4157	-	04	14	47.887	-0.43	4.15	0.009	-50.0	0.95	0	0	0
HD082734	0351F	HD082724-A0V	09	33	12.4596	-	21	06	56.601	0.2	2.83	0.031	40.7	2.09	0	0	0
HD083212	0354F	HD083104-A0V	09	36	19.9522	-	20	53	14.756	-1.64	5.61	0.025	97.5	2.83	0	0	0
HD083632	0358F	HD089239-A0V	09	40	34.0571	+	26	00	13.967	-0.85	4.72	0.069	98.3	3.4	0	0	0
HD233666	0359F	HD092728-A0III	09	42	19.4752	+	53	28	26.156	-1.62	7.37	0.040	-63.7	2.82	0	1	0
HD086986	0368F	HD089239-A0V	10	02	29.5658	+	14	33	25.189	-1.7	7.5	0.030	42.5	1.24	0	0	0
HD087141	0369F	* 39 ma-A0V	10	04	36.3229	+	53	53	30.170	0.09	4.5	0.030	-16.4	1.01	0	0	0
HD088230	0373F	HD099966-A0V	10	11	22.1405	+	49	27	15.256	-0.01	2.96	0.000	-64.0	-0.96	0	0	0
HD088446	0374F	HD023366-A0V	10	12	19.0769	+	17	17	57.044	-0.51	6.45	0.000	91.6	0.41	0	0	0
HD088725	0375F	HD097585-A0V	10	14	08.3341	+	03	09	04.677	-0.64	6.15	0.000	-60.1	-0.1	0	0	0
HD088986	0378F	HD089239-A0V	10	16	28.0831	+	28	40	56.927	0.04	4.88	0.000	27.4	0.37	0	0	0
HD089010	0379F	HD089239-A0V	10	16	32.2887	+	23	30	11.144	0.0	4.34	0.025	-48.0	0.53	0	0	0
HD091347	0389F	HD099966-A0V	10	33	50.5558	+	49	11	10.222	-0.44	6.05	0.000	-38.7	0.04	0	0	0
HD094028	0394F	HD088960-A0Vn	10	51	28.1244	+	20	16	38.960	-1.3	6.83	0.000	85.1	-0.03	0	0	0
BD-103166	0395F	BD+172473-G5	10	58	28.7798	-	10	46	13.386	0.42	8.12	0.077	63.0	-0.38	0	0	0
HD095128	0396F	HD098989-A0V	10	59	27.9728	+	40	25	48.920	0.02	3.75	0.000	18.9	0.14	0	0	0
HD096360	0400F	* 86 UMa-A0V	11	07	52.7864	+	68	21	58.864	-0.02	2.77	0.139	-124.5	2.61	0	0	0
BD+362165	0401F	HD097585-A0V	11	12	47.9995	+	35	43	43.899	-1.45	8.5	0.00 +	-154.7	0.32	0	1	0
HD097916	0405F	HD097585-A0V	11	15	54.2297	+	02	05	12.083	-0.73	8.02	0.000	61.5	0.3	0	0	1
HD097855	0406F	HD092728-A0III	11	16	04.0330	+	52	46	23.376	-0.39	5.28	0.021	-6.7	0.35	0	0	0
HD098553	0408F	HD099459-A0V	11	20	11.5950	-	19	34	40.457	-0.44	6.08	0.000	-38.0	-0.1	0	0	1
HD099109	0409F	HD097585-A0V	11	24	17.3588	-	01	31	44.664	0.4	7.16	0.088	81.3	-0.21	0	0	0
HD100906	0414F	HD101369-A0V	11	36	42.4113	-	18	58	10.585	-0.46	7.49	0.000	77.7	2.06	0	0	0
BD+511696	0419F	HD099966-A0V	11	46	35.1545	+	50	52	54.682	-1.3	8.31	0.005	102.7	-0.26	0	0	0
HD102328	0420F	HD092728-A0III	11	46	55.6221	+	55	37	41.485	0.28	2.63	0.050	58.5	1.58	0	0	0
HD102634	0421F	* 69 Leo-A0V	11	49	01.281	-	00	19	07.22	0.22	4.92	0.000	-7.4	0.53	0	0	1
HD103095	0423F	HD107655-A0V	11	52	58.7693	+	37	43	07.234	-1.21	4.37	0.000	-114.5	-0.68	0	0	0
HD104307	0427F	HD099922-A0V	12	00	42.2223	-	21	50	15.006	-0.07	3.15	0.042	96.0	2.21	0	0	0
HD105452	0431F	HD110902-A0V	12	08	24.8165	-	24	43	43.950	-0.19	3.31	0.028	-16.7	0.55	0	0	0
HD105546	0432F	HD092728-A0III	12	09	02.7208	+	59	01	05.134	-1.46	6.67	0.000	84.0	1.57	0	0	0
HD105740	0433F	HD107655-A0V	12	10	16.9638	+	16	22	13.363	-0.54	5.85	0.000	-30.9	1.33	0	0	0
HD106038	0434F	HD107655-A0V	12	12	01.3700	+	13	15	40.622	-1.25	8.76	0.000	124.5	-0.18	0	0	0
CD-2809374	0435F	HD112305-A0V	12	14	29.7453	-	29	35	55.677	-0.76	8.12	0.010	19.5	0.34	0	0	0
HD107213	0438F	HD107655-A0V	12	19	29.5259	+	28	09	24.902	0.24	5.13	0.000	5.3	0.81	0	0	0
BD+172473	0439F	HD107655-A0V	12	23	31.021	+	16	54	09.24	-1.04	8.16	0.000	54.3	-1.0	0	0	0
BD+312360	0440F	HD107655-A0V	12	24	17.400	+	30	46	48.73	-0.79	8.83	0.00	51.8	-1.0	0	0	0
HD108177	0441F	HD109309-A0V	12	25	34.9550	+	01	17	02.267	-1.41	8.35	0.000	169.6	0.08	0	1	0
HD108564	0442F	HD112304-A0V	12	28	19.1200	-	16	54	39.771	-1.0	6.9	0.016	78.0	-0.8	0	0	0
HD109443	0444F	HD101122-A0V	12	34	46.732	-	23	28	32.20	-0.6	8.16	0.035	76.6	-1.0	0	0	0
HD110885	0450F	HD116960-A0V	12	45	19.2569	+	01	03	21.097	-1.06	7.38	0.016	-50.6	2.89	0	0	1
HD111786	0453F	HD114345-A0V	12	51	57.8954	-	26	44	17.783	-1.5	5.4	0.023	-8.6	1.09	0	1	0
HD114038	0460F	HD109309-A0V	13	07	53.8123	-	10	44	25.476	-0.02	2.72	0.041	34.6	1.89	0	0	0
HD114606	0462F	HD121996-A0Vs	13	11	21.4043	+	09	37	33.519	-0.53	7.09	0.000	13.2	-0.06	0	0	0
HD114710	0463F	HD107655-A0V	13	11	52.3937	+	27	52	41.453	0.05	2.92	0.013	57.2	0.09	0	0	0
HD115589	0467F	HD112304-A0V	13	18	13.5353	-	14	34	55.555	0.28	7.62	0.082	-45.2	-0.28	0	0	0
HD115617	0468F	HD119786-A0V	13	18	24.3142	-	18	18	40.304	0.02	2.96	0.000	7.3	-0.06	0	0	0
HD116316	0471F	HD121996-A0Vs	13	22	34.1508	+	26	06	56.513	-0.51	6.42	0.002	-59.3	0.31	0	0	0
HD117200	0473F	HD143187-B8V	13	27	04.6096	+	64	44	07.890	0.03	5.7	0.011	-71.6	0.88	0	0	0
HD117176	0474F	HD121996-A0Vs	13	28	25.8086	+	13	46	43.638	-0.1	3.5	0.000	23.6	0.38	0	0	0
HD117635	0475F	HD116960-A0V	13	31	39.9375	-	02	19	02.602	-0.42	5.31	0.000	-48.1	0.03	0	0	0
HD117876	0476F	HD121996-A0Vs	13	32	48.2137	+	24	20	48.280	-0.51	3.87	0.003	20.5	1.77	0	0	0
HD118244	0479F	HD121880-A0V	13	35	11.4174	+	22	29	59.031	-0.46	5.63	0.020	75.8	0.49	0	0	0
HD119228	0481F	HD118214-A0V	13	40	44.2733	+	54	40	53.889	-0.1	0.34	0.008	-11.4	3.09	1	0	0
HD119288	0482F	HD121996-A0Vs	13	42	12.7599	+	08	23	18.226	-0.23	5.11	0.000	-44.2	0.51	0	0	0
HD120136	0485F	HD116960-A0V	13	47	15.7434	+	17	27	24.855	0.24	3.51	0.000	30.0	-1.0	0	0	0
HD120933	0487F	HD122945-A0V	13	51	47.4753	+	34	26	39.261	-0.15	-0.01	0.113	-108.7	3.38	1	0	0
HD121258	0490F	HD119752-A0V	13	54	54.6217	-	26	00	56.758	-0.2	8.8	0.283	-29.9	-1.0	0	1	0
HD125451	0504F	HD121996-A0Vs	14	19	16.2803	+	13	00	15.479	0.01	4.39	0.000	12.6	0.57	0	0	0
BD+012916	0505F	HD126129-A0V	14	21	45.2615	+	00	46	59.178	-1.86	6.47	0.03	-33.8	2.05	0	0	0
HD126141	0506F	HD121996-A0Vs	14	23	06.8213	+	25	20	17.433	-0.05	5.23	0.000	-6.0	0.53	0	0	0
HD126053	0507F	HD126129-A0V	14	23	15.2849	+	01	14	29.648	-0.37	4.64	0.000	3.3	-0.11	0	0	1
HD126614	0511F	HD132072-A0V	14	26	48.2807	-	05	10	40.007	0.52	7.06	0.055	-53.9	0.18	0	0	0
HD126778	0512F	HD127304-A0Vs	14	26	54.1638	+	28	35	20.423	-0.52	5.84	0.000	-125.1	2.01	0	0	0
HD127243	0514F	HD121409-A0V	14	28	37.8131	+	49	50	41.458	-0.78	3.16	0.060	41.2	1.9	0	1	1
BD+182890	0516F	HD121996-A0Vs	14	32	13.4854	+	17	25	24.290	-1.54	7.74	0.020	84.5	1.34	0	0	0
HD128959	0521F	HD131885-A0V	14	40	43.3622	-	26	43	46.937	-0.51	7.57	0.050	17.1	0.82	0	0	0
HD130095	0523F	HD119752-A0V	14	46	51.2120	-	27	14	53.958	-1.7	7.8	0.068	112.6	1.31	0	0	0
HD130322	0524F	HD131951-A0V	14	47	32.724	-	00	16	53.32	0.12	6.23	0.025	-43.5	-0.26	0	0	0
HD130817	0525F	HD127304-A0Vs	14	49	06.7425	+	37	48	40.243	-0.29	5.08	0.013	-40.4	0.64	0	0	0
HD130705	0526F	HD131951-A0V	14	49	26.1554	+	10	02	38.965	0.34	3.95	0.000	-53.0	1.79	0	0	0
HD132142	0529F	HD121409-A0V	14	55	11.0434	+	53	40	49.260	-0.37	5.8	0.000	19.3	-0.38	0	0	0
HD132475	0534F	HD138813-A0V	14	59	49.7651	-	22	00	45.809	-1.37	6.91	0.000	143.4	0.49	0	0	0
BD+302611	0538F	HD127304-A0Vs	15	06	53.8278	+	30	00	36.941	-1.45	6.09	0.01	-287.5	2.47	0	0	0
HD134063	0539F	HD131951-A0V	15	07	15.4405	+	22	33	51.695	-0.69	5.47	0.019	-89.7	1.49	0	0	0
HD134083	0540F	HD131951-A0V	15	07	18.0660	+	24	52	09.101	-0.01	3.86	0.000	-9.4	0.47	0	0	0
HD134169	0541F	HD140775-A0V	15	08	18.0580	+	03	55	50.128	-0.81	6.16	0.000	4.5	0.4	0	1	0
HD134440	0542F	HD134013-A0V	15	10	12.9689	-	16	27	46.516	-1.34	7.19	0.000	322.2	-0.84	0	0	0
HD134439	0543F	HD134013-A0V	15	10	13.0880	-	16	22	45.860	-1.27	7.04	0.005	289.5	-0.71	0	0	1
HD134987	0544F	HD138295-A0V	15	13	28.6670	-	25	18	33.646	0.26	4.88	0.026	2.9	-1.0	0	0	0
HD136064	0545F	HD143187-B8V	15	14	38.3401	+	67	20	48.197	0.03	3.87	0.010	-47.0	0.58	0	0	0
HD136202	0550F	HD140755-A2	15	19	18.7971	+	01	45	55.468	0.05	4.01	0.030	33.5	0.61	0	1	0
HD137391	0553F	HD127304-A0Vs	15	24	29.4283	+	37	22	37.757	0.1	3.62	0.004	-603.0	-1.0	0	0	0
HD137471	0555F	HD140729-A0V	15	25	47.3975	+	15	25	40.930	-0.04	1.04	0.034	-28.7	3.07	0	0	0
HD138290	0559F	HD140729-A0V	15	30	55.4332	+	08	34	44.737	-0.1	5.66	0.015	-35.9	0.65	0	0	0
HD138776	0562F	HD140775-A0V	15	34	16.9188	-	02	43	26.643	0.35	7.11	0.069	7.0	0.17	0	0	0
HD139641	0565F	HD127304-A0Vs	15	37	49.5979	+	40	21	12.363	-0.51	3.1	0.020	20.7	1.31	0	0	0
BD+053080	0569F	HD140775-A2	15	45	52.4015	+	05	02	26.558	-0.44	6.88	0.00	-17.9	-0.26	0	0	0
HD142575	0574F	HD140775-A0V	15	55	02.8379	+	05	04	12.148	-0.7	7.51	0.019	-55.0	0.9	0	0	0
HD142703	0577F	HD138062-A0V	15	56	33.3736	-	14	49	45.976	-1.1	5.34	0.036	9.2	0.86	0	1	0
HD144585	0584F	HD148968-A0V	16	07	03.3694	-	14	04	16.665	0.29	4.8	0.014	-45.1	0.28	0	0	0
HD145148	0586F	HD140755-A2	16	09	11.2145	+	06	22	43.302	0.1	3.68	0.000	-0.2	0.53	0	0	0
HD145976	0589F	HD145122-A0Vnn	16	12	45.4709	+	26	40	14.094	-0.02	5.48	0.018	-8.3	1.04	0	0	0
BD+112998	0598F	HD140775-A0V	16	30	16.7825	+	10	59	51.748	-1.01	7.18	0.024	69.8	1.26	0	0	0
HD149009	0603F	HD164899-A0Vs	16	31	13.4310	+	22	11	43.649	0.09	2.04	0.075	-28.0	2.84	1	0	0
HD150177	0611F	HD159415-A0V	16	39	39.1298	-	09	33	16.512	-0.58	4.98	0.000	-46.7	0.6	0	0	0
HD152601	0616F	HD148968-A0V	16	54	35.6932	-	06	09	14.333	0.1	2.8	0.023	-45.0	1.65	0	0	0
HD152781	0617F	HD149134-A0V	16	56	01.8443	-	16	48	22.553	0.08	4.26	0.048	-19.3	0.79	0	0	1
HD154733	0620F	HD165029-A0V	17	06	18.0476	+	22	05	02.955	-0.09	2.48	0.018	-127.4	1.98	0	0	0
HD155763	0621F	HD143187-B8V	17	08	47.1959	+	65	42	52.863	-0.11	3.55	0.030	23.6	2.58	0	0	0
HD155358	0622F	HD157778-A0Vn	17	09	34.6174	+	33	21	21.085	-0.63	5.81	0.000	15.7	0.3	0	0	1
HD157089	0628F	HD161289-A0V	17	21	07.0556	+	01	26	34.988	-0.57	5.42	0.000	-133.8	0.26	0	0	0
HD157881	0630F	HD161289-A0V	17	25	45.2326	+	02	06	41.120	-0.01	4.37	0.000	-54.4	-0.95	0	0	0
HD159482	0636F	HD161289-A0V	17	34	43.0609	+	06	00	51.574	-0.75	6.79	0.004	-103.1	-0.02	0	0	1
HD160693	0639F	HD164899-A0Vs	17	39	36.8724	+	37	11	01.506	-0.56	6.9	0.000	23.7	0.06	0	0	1
HD161149	0641F	HD165029-A0V	17	43	22.0221	+	14	17	42.604	0.33	5.1	0.043	-53.5	-1.0	0	0	0
HD162211	0648F	HD165029-A0V	17	48	49.1464	+	25	37	22.329	-0.06	2.4	0.001	-42.5	1.65	0	0	0
HD164349	0654F	HD165029-A0V	18	00	03.4160	+	16	45	03.309	-0.01	1.94	0.001	-35.8	2.88	0	0	0
HD166460	0667F	HD161289-A0V	18	10	40.2995	+	03	19	27.325	-0.05	2.58	0.023	10.1	2.15	0	0	0
HD170737	0679F	HD174567-A0Vs	18	29	54.1103	+	26	39	26.247	-0.77	5.95	0.025	-110.8	0.88	0	0	0
HD171496	0683F	HD177213-A0V	18	36	07.4940	-	24	26	11.320	-0.73	5.59	0.151	-18.1	1.55	0	0	0
HD173740	0690F	HD172728-A0V	18	42	46.9665	+	59	37	36.347	-0.34	5.0	0.001	16.6	-2.06	0	0	0
HD173819	0697F	HD170654-A0V	18	47	28.9498	-	05	42	18.541	-0.67	2.16	0.260	19.3	4.27	1	0	0
HD174912	0699F	HD174567-A0Vs	18	51	25.1791	+	38	37	35.654	-0.45	5.68	0.000	3.3	0.03	0	0	0
HD175535	0703F	CCDM J19302+5639AB-A0V	18	53	13.5416	+	50	42	29.585	-0.07	2.82	0.007	-18.6	2.25	0	0	0
HD175588	0704F	HD174567-A0Vs	18	54	30.2833	+	36	53	55.013	-0.14	-1.25	0.000	-27.0	4.06	0	0	1
HD175640	0706F	HD171149-A0Vn	18	56	22.6604	-	01	47	59.505	0.17	6.25	0.044	24.4	1.84	0	0	0
NGC6791-R4	0940C	HD174567-A0Vs	19	20	49.7000	+	37	43	41.2	0.42	7.82	0.119	-45.5	2.78	0	0	0
NGC6791-R19	0943C	HD174567-A0Vs	19	20	52.8000	+	37	44	26.900	0.42	10.19	0.119	-41.2	2.03	0	0	0
HD182572	0721F	HD182761-A0V	19	24	58.2002	+	11	56	39.886	0.34	3.04	0.031	608.6	-1.0	0	0	0
CD-2415398	0723F	HD177120-A0V	19	32	20.7821	-	23	51	12.755	-1.17	9.06	0.097	17.7	3.17	0	0	1
HD184499	0726F	HD174567-A0Vs	19	33	27.0812	+	33	12	06.716	-0.54	5.08	0.000	-123.8	0.31	0	0	1
HD185657	0730F	HD178207-A0Vn	19	37	56.7133	+	49	17	03.902	-0.19	4.09	0.000	-55.6	1.74	0	0	0
HD186408	0733F	HD194354-A0Vs	19	41	48.9534	+	50	31	30.215	0.08	4.43	0.000	-54.8	0.2	1	0	0
M71_1-77	0967C	* 5 Vul-A0V	19	53	37.4000	-	1	-1	-1	-0.22	12.11	0.270	26.4	1.58	1	0	0
M71_I	0971C	* 5 Vul-A0V	19	53	44.6000	+	18	46	35.0000	-0.78	8.66	0.270	-9.0	2.71	0	0	0
HD188510	0742F	HD182919-A0V	19	55	09.6783	+	10	44	27.372	-1.43	7.13	0.000	-134.7	-0.39	0	1	0
HD189558	0747F	HD182678-A0V	20	01	00.2457	-	12	15	20.340	-1.04	6.16	0.000	-1.6	0.47	0	0	0
HD190360	0749F	HD192538-A0V	20	03	37.4058	+	29	53	48.494	0.21	4.08	0.000	-55.4	0.01	0	0	0
HD190178	0752F	HD195549-A0V	20	04	49.4677	-	28	16	25.164	-0.66	8.07	0.002	22.8	0.64	0	0	0
HD191046	0755F	HD192538-A0V	20	06	28.9887	+	36	13	35.918	-0.75	4.19	0.040	-84.5	2.5	0	0	1
HD345957	0757F	HD182919-A0V	20	10	48.1619	+	23	57	54.514	-1.2	7.36	0.000	-74.7	0.35	0	0	0
HD192640	0759F	HD192538-A0V	20	14	32.0333	+	36	48	22.692	-0.8	4.42	0.026	-0.6	1.18	0	0	0
HD192909	0760F	HD199217-A0V	20	15	28.3228	+	47	42	51.160	-0.02	0.16	0.016	-61.8	3.78	1	0	0
HD196755	0768F	HD198070-A0Vn	20	39	07.7843	+	10	05	10.338	-0.02	3.61	0.014	-85.0	0.76	0	0	0
BD+044551	0777F	HD198070-A0Vn	20	48	50.7212	+	05	11	58.801	-1.26	8.25	0.00	-82.7	1.63	1	0	0
HD199191	0779F	HD205314-A0V	20	53	18.3149	+	54	31	05.164	-0.7	4.73	0.010	-207.3	1.54	0	0	0
HD200527	0782F	HD201076-A0V	21	02	24.1998	+	44	47	27.523	-0.07	1.09	0.000	-9.7	3.21	0	0	0
HD200779	0785F	HD210501-A0V	21	05	19.7452	+	07	04	09.477	0.02	5.31	0.003	-47.6	-0.76	0	0	0
HD201891	0790F	HD208108-A0Vs	21	11	59.0315	+	17	43	39.890	-1.05	5.93	0.000	-86.8	0.03	0	0	0
HD201889	0791F	HD210501-A0V	21	11	59.5235	+	24	10	05.389	-0.74	6.43	0.000	-83.9	0.31	0	0	1
HD203638	0795F	HD202025-A0V	21	24	09.5924	-	20	51	06.740	0.12	2.69	0.010	6.4	1.7	0	0	0
HD204041	0796F	HD198070-A0Vn	21	25	51.5837	+	00	32	03.620	-0.44	5.96	0.025	29.3	0.96	0	1	0
HD204155	0798F	HD20722-A0 D	21	26	42.9055	+	05	26	29.902	-0.69	7.01	0.000	-49.5	0.31	0	0	0
HD204613	0799F	HD205314-A0V	21	27	42.9678	+	57	19	18.861	-0.38	6.79	0.008	-102.9	0.33	0	0	0
HD204587	0804F	HD203893-A0V	21	30	02.7541	-	12	30	36.255	-0.11	5.88	0.004	-86.4	-0.86	0	0	0
HD205153	0806F	HD202941-A0V	21	34	09.1873	-	27	54	04.333	0.07	6.83	0.025	-27.5	0.97	0	0	0
HD205512	0807F	HD209932-A0V	21	34	46.5638	+	38	32	02.604	0.03	2.6	0.000	-108.5	1.69	0	0	0
HD206078	0808F	HD201184-A0V	21	37	10.4225	+	62	18	15.283	-0.59	4.72	0.002	-120.4	1.61	0	1	0
HD206453	0811F	HD201184-A0V	21	42	39.5071	-	18	51	58.766	-0.41	2.55	0.033	40.2	-1.0	1	0	0
HD207222	0818F	HD208108-A0Vs	21	46	56.2591	+	21	17	50.768	-0.36	8.37	0.057	-7.0	1.11	0	0	0
HD210295	0825F	HD215143 - B7.5V	22	09	41.4440	-	13	36	19.478	-1.26	7.18	0.000	-23.9	0.98	0	0	0
HD211075	0830F	HD208108-A0Vs	22	14	20.0378	+	18	01	13.370	-0.42	5.22	0.016	33.5	2.14	1	1	0
HD213042	0835F	HD220455-A0V	22	29	15.2354	-	30	01	06.271	0.12	5.11	0.076	13.5	-0.63	0	0	0
HD216174	0845F	HD219290-A0V	22	49	46.3148	+	55	54	09.999	-0.61	2.63	0.030	-47.4	2.03	0	0	0
HD216131	0846F	BD+3904890-A0V	22	50	00.1931	+	24	36	05.698	-0.07	1.18	0.000	87.9	1.69	0	0	0
HD217107	0855F	HD215143-B7.5V	22	58	15.5411	-	02	23	43.384	0.33	4.54	0.019	10.9	0.01	0	0	0
HD218640	0861F	HD223352-A0Vnp	23	09	54.896	-	22	27	27.44	0.36	2.95	0.021	25.0	-1.0	0	0	0
HD219449	0867F	HD219833-A0V	23	15	53.4948	-	09	05	15.854	0.03	1.6	0.000	-22.1	1.78	0	1	0
HD219623	0868F	HD211301-A0V	23	16	42.3033	+	53	12	48.510	0.07	4.31	0.000	17.0	0.1	0	0	1
HD219615	0870F	HD215143-B7.5V	23	17	09.9374	+	03	16	56.238	-0.57	1.39	0.000	1.8	1.81	0	0	1
HD219734	0871F	HD219290-A0V	23	17	44.6471	+	49	00	55.081	-0.04	0.51	0.019	12.1	3.08	0	0	0
HD219978	0873F	HD223386-A0V	23	19	23.7734	+	62	44	23.185	0.18	0.79	0.228	-27.4	3.92	0	1	0
HD220009	0874F	HD210501-A0V	23	20	20.5831	+	05	22	52.701	-0.8	1.99	0.000	85.4	2.43	0	1	0
HD221148	0881F	HD215143-B7.5V	23	29	32.0820	-	04	31	57.891	0.34	3.89	0.000	0.5	0.8	0	0	0
HD221377	0883F	HD219290-A0V	23	31	19.7259	+	52	24	38.504	-0.6	6.37	0.005	37.3	0.64	0	0	0
HD221830	0886F	HD210501-A0V	23	35	28.8937	+	31	01	01.830	-0.4	5.3	0.000	-71.4	0.2	0	0	0
G171-010	0890F	HD219290-A0V	23	41	54.989	+	44	10	40.78	0.09	5.93	0.088	-36.3	-2.62	0	0	0
HD223524	0893F	HD219833-A0V	23	50	14.7298	-	09	58	26.893	0.02	3.22	0.013	2.5	1.67	0	0	0
HD224458	0895F	HD006457-A0Vn	23	58	06.2501	+	29	58	35.906	-0.44	5.73	0.050	-114.2	1.55	0	0	0

Equations

$$f_{\lambda }^{\mathrm{cor}}(\lambda )=f_{\lambda }(\lambda )\times 10^{(0.4\times A_{\lambda })},$$

$$A_{\lambda }=1.056\times E(B-V){\lambda }^{-1.84}.$$

$$f(C_X)=10^{(X_{\mathrm{syn}}-{\mathcal{N}}_{X_{\mathrm{obs}}})/2.5},$$

$$⟨C⟩=\frac{{\sum }_X{w}_X\mathrm{Peak}[f(C_X)]}{{\sum }_X{w}_X},$$

$$\log g={\log }_{10}\left(\frac{6.6743\times 10^{-8}\times M\times 1.989\times 10^{33}}{(R\times 6.955\times 10^{10}{)}^2}\right),$$

$$\begin{array}{rl}\log F_{\nu }=& a_0+a_{1}t+a_{2}z+a_{3}g+a_4{z}^2+a_5{t}^2+a_6{g}^2+\\ & a_7(t\times z)+a_8(t\times g)+a_9(z\times g)+a_{10}{z}^3+\\ & a_{11}{t}^3+a_{12}{g}^3+a_{13}(t^2\times z)+a_{14}(z^{2}t)+\\ & a_{15}(g\times t^2)+a_{16}{t}^4+a_{17}{z}^4+a_{18}(t^2\times z^2)+\\ & a_{19}(t^3\times z)+a_{20}{t}^5.\end{array}$$

$$\begin{array}{rl}\log F_{\nu }=& a_0+a_{1}t+a_{2}z+a_{3}g+a_4{t}^2+\\ & a_5{g}^2+a_6{z}^2+a_7(z\times g)+a_8(t\times g)+\\ & a_8(t\times z)+a_9{t}^3+a_{10}{g}^3+a_{11}{z}^3+\\ & a_{12}(t\times g\times z)+a_{13}(t\times t\times z)+\\ & a_{14}(t\times t\times g)+a_{15}(z^2\times t)+a_{16}(z^2\times g)+\\ & a_{17}(t\times g^2)+a_{18}(z\times g^2)+a_{18}{t}^4.\end{array}$$

$$\begin{array}{rl}\log F_{\nu }=& a_0+a_{1}t+a_{2}z+a_{3}g+a_4{t}^2+a_5{g}^2+a_6{z}^2+\\ & a_7(t\times z)+a_8(t\times g)+a_9{t}^3+a_{10}(t\times g^2)+a_{11}{z}^3+\\ & a_{12}(t^2\times g)+a_{13}(t^2\times z)+a_{13}(t\times z^2)+\\ & a_{14}(t\times g\times z)+a_{15}(g\times z^2)+a_{16}{t}^4+a_{17}{g}^4+\\ & a_{18}(t^3\times g)+a_{20}(z\times t^3)+a_{21}(z^2\times t^2)+\\ & a_{21}(z^3\times t)+a_{22}(t^2\times g{)}^2)+a_{23}(z\times t^2\times g)+\\ & a_{24}{t}^5.\end{array}$$

$$\begin{array}{rl}\log F_{\nu }=& a_0+a_{1}t+a_{2}z+a_{3}g+a_4{t}^2+a_5{g}^2+a_6{z}^2+\\ & a_7(t\times z)+a_8(t\times g)+a_9(g\times z)+a_9{t}^3+a_{10}{g}^3+\\ & a_{11}{z}^3+a_{12}(t^2\times z)+a_{13}(t\times z^2)+a_{14}(g\times t^2)+\\ & a_{15}(g^2\times t)+a_{16}{t}^4+a_{17}{z}^4+a_{18}(t^2\times z^2)+\\ & a_{19}(t^2\times g^2)+a_{20}(z^2\times g^2)+a_{21}{t}^5.\end{array}$$

$$\begin{array}{rl}\log F_{\nu }=& a_0+a_{1}t+a_{2}z+a_{3}g+a_4{t}^2+a_5{z}^2+a_6{g}^2+\\ & a_7(t\times g)+a_8(t\times z)+a_9(g\times z)+a_{10}{t}^3+a_{11}{g}^3+\\ & a_{12}{z}^3+a_{13}(t\times g\times z)+a_{14}(t^2\times z)+a_{15}(t^2\times g)+\\ & a_{16}(z^2\times g)+a_{17}(t\times g^2)+a_{18}(z\times g^2)+a_{19}{t}^4.\end{array}$$

Full text

I. Introduction

Stellar libraries, whether empirical or theoretical, are foundational to several different fields of astrophysics. In stellar population synthesis (SPS) models stellar libraries are needed to convert the stellar evolution predictions of stellar parameters: effective temperature ($T_{\rm eff}$), surface gravity (${\rm log}g$), and metallicity ([Fe/H]), into spectral energy distributions (SEDs) (conroy2013). Stellar spectra can be used to compute the line-of-site velocity distributions in galaxies (cappelari2004; emsellem2004). Well-characterized stellar spectra are also a key ingredient in exoplanet studies (e.g, newton2014; mann2015).

The goal for any stellar library is extensive coverage in stellar parameter space and large wavelength coverage at comparable or better resolution than typical observations to which they are compared. Large wavelength coverage is important because different wavelength regimes probe different stellar populations in the integrated light of galaxies. The optical is the most well-studied wavelength regime but there is important information that is only available in other regimes. For example, the ultra-violet (UV) probes the populations of hot, massive stars (e.g., vazdekis2016, and the references therein) and the near infrared (IR) probes the populations of cool, evolved stars such as those on the asymptotic giant branch (athey2002; martini2013; villaume2015; simonian2016). Furthermore, the endeavor to characterize biological signatures of exoplanets must consider the effect and characteristics of the host stars, which requires UV-IR coverage (france2015). Moreover, uniform coverage in parameter space is also necessary to ensure accurate stellar population models. Unfortunately, there is still no single stellar library that covers the entire range of wavelength and parameter space.

Empirical stellar libraries have been available for over 30 years (e.g., gunn1983; pickles1985; diaz1989; silva1992; pickles1998; worthey1994; jones1999; lancon2000; cenarro2001; prugniel2001; leborgne2003; valdes2004; sanchez2006; marm2008; rayner2009; ardila2010; sharon2010). A key limitation of existing stellar libraries is their often limited coverage in stellar parameter space. This is in some respects a fundamental problem because not all stars of interest are close enough to enable detailed observations (e.g., hot metal poor stars). Standard observational constraints such as atmospheric absorption and sky emission, which is especially prominent in the IR, flux calibration, wavelength coverage, and spectral resolution further challenge the development of comprehensive empirical stellar libraries.

Theoretical libraries offer the advantage of dense coverage in parameter space, arbitrarily high spectral resolution, and no need to correct for atmospheric absorption or flux calibration (e.g., munari2005; martins2005; coelho2005). However, theoretical stellar libraries are only as good as the available atomic and molecular line lists and the approximations made in computing the models, e.g., the assumption of local thermodynamic equilibrium (LTE) and 1D plane-parallel atmospheres. The effect of non-LTE is generally taken into account where it matters most (e.g., hot stars and metal-poor stars lanz2003; lind2012) and some 3D theoretical models (e.g, magic2013) have begun to emerge but these techniques have not been widely adopted due to the fact that they are very computationally expensive. Theoretical stellar spectra are most unreliable for very cool stars and very hot stars (allard1997; martins2007; bertone2008; allard2013; rajpurohit2014; rajpurohit2016). The former is a particularly acute problem for both exoplanet and galaxy studies. All the habitable zone planes found by TESS will be around M dwarfs (france2015) and counting cool dwarf stars in the absorption lines of integrated spectra of galaxies has emerged as a way to constrain the initial mass function (IMF) (spinrad1962; wing1969; cohen1978; frogel1978; kleinmann1986; diaz1989; ivanov2004; cvd2012) in unresolved stellar populations. The limitations of the theoretical stellar spectra in the cool star regime makes it necessary to turn to empirical stellar libraries.

sanchez2006 created a landmark empirical optical stellar library, the MILES library. The MILES library, consisting of nearly 1000 stars, covers a wide range of stellar parameter space over the wavelength range $0.35-0.75\mu m$. The MILES library enabled the creation of more precise SPS models which in turn facilitated a greater understanding of galaxies beyond the reach of resolved stellar population studies.

However, as stated previously, the optical window does not contain a complete picture of a stellar population. A major advance occurred with the release of the rayner2009 Infrared Telescope Facility (IRTF) spectral library. The creation of this near-IR library was a great step forward for SPS models (e.g., cvd2012; spiniello2012; meneses2015; rock2016). A limitation of the IRTF stellar library is its narrow stellar parameter range, all stars being around solar-metallicity. Furthermore, there is very little overlap in the stars between the MILES and IRTF stellar libraries. The X-Shooter Spectral Library (XSL) is observing many stars with continuous spectral coverage from $0.35-2.5\mu m$ and will be another valuable library once complete (e.g., chen2014).

In this work we present the Extended IRTF Library. The extension is two-fold: we expanded the metallicity coverage to $-1.7<$[Fe/H] $<0.6$ a large expansion from the just solar-metallicity coverage of the original IRTF library, and we selected all of our objects from the MILES stellar library to provide continuous coverage from the optical through near-IR. In addition to the new stellar library we also present an interpolator that uses a data-driven model created from the new stellar library. The interpolator generates a stellar spectrum as a function of $T_{\rm eff}$, log$g$, and [Fe/H]. This interpolator provides smooth variation in stellar spectra across parameter space, and is an important component in the creation of stellar population models.

The rest of this paper is organized in the following manner: Section 2 details our sample selection, observational strategy, data reduction, and characteristics of the objects and data. In Section 3 we describe our interpolator and assess its quality. In Section 4 we explore the behavior of the library and the interpolator and compare both to theoretical predictions. Finally, in Section 5 we summarize the main points of this work.

II. The Extended IRTF Library

II.1. Sample Selection

We selected our target stars from the MILES stellar library (sanchez2006), avoiding known spectroscopic binary stars, to provide continuous coverage from the optical to the near-IR. We selected our targets to span a stellar parameters that would enable the creation of stellar population models for intermediate and old population ages as determined with stellar isochrones from the MIST project (choi2016) .

In Figure 1 we compare the MILES coverage in $T_{\rm eff}$-${\rm log}g$ space and the stars observed with IRTF for this work. Each panel shows the stars in a given metallicity bin where the stars from the MILES library are represented as blue circles and the stars observed for this library are represented as red circles. Each panel also displays 13.5 Gyr (black line) and 3 Gyr (grey line) MIST isochrones. Selecting targets by eye, we achieved relatively uniform coverage along the intermediate age isochrones for all but the lowest metallicity bins and the old age isochrones across all the metallicity bins. In particular, we have well sampled turn-offs for all except the intermediate-age, low-metallicity stellar tracks. The metallicity distribution of the library is summarized in panel f of Figure 1.

Throughout this work we use the stellar parameters determined by prugniel2011 and sharma2016 instead of those reported by cenarro2007. The stellar parameters determined by cenarro2007 were determined heterogeneously, depending on which additional literature data was available for a given star. As a result, the stellar parameters from cenarro2007 vary in quality and trustworthiness. prugniel2011 sought to revise the stellar parameters of the stars in the MILES library in a more robust and homogeneous way. They used ELODIE spectra to perform full-spectrum $\chi^{2}$ minimization fits (koleva2009) between the MILES spectra and templates built from the ELODIE 3.2 library (wu2011). sharma2016 revised the stellar parameter values of MILES library stars with $T_{\rm eff}<4800$ K with an improved interpolator.

It is important to note that the accuracy of SPS models is predicated upon the accuracy of the stellar parameters. percival2009 found that a change of 100 K in the effective temperature of stars in a stellar library can propagate into a 20% error in absolute ages estimated from stellar population models. Furthermore, derived exoplanet properties are a direct function of the stellar parameters of the host star (e.g., mann2015). These examples underly the need for accurate stellar parameters in empirical stellar libraries.

We do not make use of the rayner2009 library (except for comparison with re-observed stars) for two reasons. First, as we will discuss later, the detectors on SpeX have been upgraded since the IRTF library of rayner2009. A significant component of the upgrade included a blueward extension to $0.70\mu m$. The original IRTF library had a blue cutoff of $0.8\mu m$, which meant that there was no overlap with the red cutoff of the MILES library. Second, there were few stars that were in both the MILES stellar library and the rayner2009 library. Our requirement for continuous coverage from the optical to the near-IR for a common set of stars led us to not make use of the original IRTF library.

II.2. Observations

We carried out 24 nights of observations from August 2014 to June 2016 using the upgraded SpeX instrument on IRTF. For details on SpeX we refer the reader to rayner2003. In short, SpeX is a medium-resolution, cross-dispersed spectrograph equipped with a 2048x2048 Hawaii-2RG array. All stars were observed in the short-wavelength cross-dispersed mode (SXD) using the $0\arcsec.3$ (2 pixel) slit, providing a nominal resolving power of R$\sim$2000. We observed every star at the parallactic angle. The upgraded detectors extended the wavelength coverage further into the blue, giving a wavelength range from $0.7-2.55\mu m$. The upgraded detectors also remove the 0.06 $\mu$m gap that used to exist between the $H$ and $K$ bands (rayner2009).

An A0 V star (or a star of similar spectral type) was observed either before or after each science object to correct for absorption due to the Earth’s atmosphere and to flux calibrate the science object spectra. For most stars the airmass difference between the target star and the standard star was less than 0.1. Standard stars were also chosen to be located within 10 degrees of the target object whenever possible, to minimize the effects of any differential flexure in the instrument between the observations of the target and standard. Due to a shortage of standard stars near some targets, in a few cases airmass differences between the two reached 0.15.

We took a set of internal flat field and argon arc lamp exposures with each target-standard pair. This procedure helps minimize the possible effects of flexure of the detector on the quality of the flat-fielding and the final wavelength solution.

A table summarizing the content of the library including the object names, $K_{S}$-band magnitudes, associated telluric standard stars, and various other characteristics for all the 284 library stars is presented in Table A.

II.3. Data Reduction

Data were reduced following the same procedure described in rayner2009 using the facility IDL-based reduction package for SpeX, Spextool v4.0.4 (cushing2004). cushing2004 provides a comprehensive explanation of the data reduction process and so here we summarize and highlight the main steps.

The science images were processed by correcting for nonlinearity, subtracting the pairs of images taken at two different slit positions, and dividing the pair-subtracted images by a normalized flat field. Any residual sky signal left over from the pair subtraction is removed from the image and the spectra in individual orders were then optimally extracted. Argon lines were used to wavelength calibrate the data. For the SXD observing mode, several arc exposures are combined to increase the signal-to-noise ratio (SNR).

We used the A0 V standard star observed with each science object to correct for the telluric absorption and flux calibrate the science object using the method described by vacca2003. In brief, the method uses a theoretical spectrum of Vega to determine the intrinsic spectrum of any A0 V star by scaling and reddening the Vega model to match the near-IR magnitudes of the observed A0 V stars and modifying the model to account for differences in line strengths, radial and rotational velocities, and spectral resolution. This method also corrects for instrument throughput and flux calibrates the spectra of the target stars.

In Figure 2 we show the SpeX spectrum for the library star BD+0503080 before (blue) and after (red) the telluric correction. The before and after spectra have been vertically scaled to clarify the comparison. Also shown is atmospheric transmission at Maunakea for an airmass of 1.5 and precipitable water vapor of 3mm (lord1992). The before spectrum has areas of very low signal and features in wavelength regions that align with the deepest parts of absorption in the atmospheric transmission spectrum. The red line demonstrates that much of the noise in this region is decreased after the telluric correction. We subsequently mask the regions in the IRTF spectra where the atmospheric absorption is most prominent, 1.32 $\mu$m-1.41$\mu$m and 1.82$\mu$m-1.94$\mu$m.

This telluric correction procedure is quite effective in removing the effects of the atmosphere. However, A0 V stars have prominent hydrogen absorption lines and weak metal features, which can complicate the telluric correction. In Figure 3 we show a theoretical spectrum of an A0 V star (purple) comparef to an atmospheric transmission (black, the model for the first three panels is from lord1992 and the model for the fourth panel is from clough2005), and an example of a telluric spectrum used to correct the library stars (grey). Both the A0 V and transmission spectra have been degraded to a resolution of $R\equiv 2000$. The top panel shows the region around the Paschen break, which can be particularly difficult to fit with models at the percent level. We also see that there are features in the telluric spectrum that are likely spurious and are associated with the metal lines in A0 V stars. We have labeled several of the metal features in Figure 3. Our telluric correction method also relies on modeling and removing the A0 V spectrum by modifying the model spectrum of Vega to match the A0 V star. This method is better than interpolating over the hydrogen lines, as there are telluric features at those wavelengths, but there are imperfections to this process. We address the uncertainties associated with these difficulties shortly. The telluric correction appears to be well-behaved in regions away from hydrogen lines and the weak metal lines.

After the telluric correction the spectra extracted from different orders were merged into a single, continuous spectrum. In rayner2009 an additional scale factor was needed to match the flux levels of the different orders but the updates to the SpeX detector made this step unnecessary. All wavelengths are in vacuum. Spextools provides a measure of uncertainty for each reduced spectrum and the typical formal SNR of the library is very high with a mean value $\sim 500$. However, the quoted SNR only includes statistical (photon counting) uncertainty, not correlated noise or any source of systemic uncertainty. Most importantly, we are interested in the uncertainty our telluric correction method introduces (see above).

To empirically measure the uncertainty of the library stars we compare five stars with repeat observations: HD007106, HD021197, HD138776, HD201891, and HD204613. For all of these observations we followed the same observing and reduction strategies as described above. The repeat observations were done with the same standard star. We computed the difference between the normalized spectra of the same star and divided by a factor of $\sqrt{2}$ (black line in Figure 4). The Poisson uncertainty is the inverse of the wavelength-dependent average of the SNR for each pair of target observations (red line in Figure 4).

While Figure 4 demonstrates that the Poisson uncertainty underpredicts the empirical uncertainty for most of the wavelength range, the empirical uncertainty is almost always $\sim 0.2-0.3\%$. The exceptions to this are in regions heavily affected by telluric absorption (upper-right and lower left panels) or where there are many broad hydrogen absorption and metal lines in the A0 V standard stars (upper-left panel). Still, even in these regions the uncertainty is 1-2%.

The empirical uncertainty presented here encompasses differences in weather and/or observing conditions, potential human error in the reduction process, and correlated noise. It does not assess the uncertainty associated with using different standard stars or using different techniques for telluric correction (e.g. vd2012; kausch2015). It is not known what effect using a different telluric correction technique would have on the quality of SpeX spectra. Assessing the impact of these additional sources of uncertainty is beyond the scope of this work but will be pursued in the future.

To demonstrate the quality of the individual features, noise in the continuum after the full reduction, and qualitative metallicity trends we show a sequence of stars ordered by metallicity over the $IYJHK$ photometric bands in Figures 5-9. The left-panel shows stars roughly on the main-sequence turn-off and the right-panel shows stars roughly on the subgiant branch. We highlight a selection of prominent lines in each bandpass. We qualitatively see general trends with metallicity. However, we are not completely controlling for temperature and surface gravity effects and so it is difficult to say anything definitively about potential trends. In Section 4 we look at equivalent width trends as a function of temperature and surface gravity.

II.3.1 Correcting to Restframe Wavelength

We used the code Prospector (Johnson et al. in prep)111https://github.com/bd-j/prospector to determine line-of-sight velocities for each star, which were used to correct the final reduced spectra to the restframe. Prospector is a code for inference of physical parameters from spectroscopic data via MCMC sampling of the posterior probability distributions. To obtain estimates of the posterior velocity distribution using prospector, a spectral model is constructed for each star by linearly interpolating the C3K theoretical spectral models222This is the theoretical library described in cvd2012 with some minor updates to the line lists. to the prugniel2011 and sharma2016 parameters, and then broadened to the resolution of IRTF. At each MCMC step this spectrum is shifted in velocity and the likelihood of the data given the redshifted model is calculated, after masking regions of strong telluric lines.

II.4. Flux Calibration

To de-redden the flux calibrated spectra we used the $E(B-V)$ values given in the MILES stellar library (P. Sánchez-Blázquez, private communication),

[TABLE]

where $f_{\lambda}(\lambda)$ is the observed spectrum and $A_{\lambda}$ is the extinction law as a function of wavelength. We adopted the near-IR law given by fitzpatrick2007 with $R_{V}=3.1$,

[TABLE]

The MILES spectra were de-reddened using the same $E(B-V)$ values.

We absolutely flux calibrated the IRTF spectra using a correction factor based on 2MASS $JHK_{S}$ photometry. We computed the correction factor for each star by using the reported 2MASS magnitude, $\mu$, and error, $\sigma$, to create a random normal distribution for each bandpass, $\mathcal{N}\left(\mu,\sigma^{2}\right)_{X_{\rm obs}}$, where $X$ denotes a given bandpass. We created a distribution of calibration factors using the following expression,

[TABLE]

$X_{\rm syn}$ is the AB synthetic magnitude computed from the spectrum. The observed spectrum for each star is multiplied by a single correction factor,

[TABLE]

where the weight, $w_{X}$, is the inverse variance given by the $1\sigma$ deviations from $f(C_{X})$, and ${\rm Peak}[f(C_{X})]$ is the peak of the distribution of calibration factors. As in rayner2009, this scaling has the effect of shifting the entire spectrum up or down so that the overall absolute flux level is correct, while simultaneously preserving the relative flux calibration of each spectral order derived from the observations and telluric correction procedures.

The publicly available MILES spectra are normalized to unity so in addition to absolutely flux calibrating the IRTF spectra we needed to absolutely flux calibrate the MILES spectra. We corrected the MILES spectra in a similar manner to the IRTF spectra using the average of the available $BV$ photometry. We preferentially used Tycho (hog2000a; hog2000b) $B_{T}V_{T}$ photometry and for stars where that is not available we used Johnson $BV$ photometry taken from Simbad. However, uncertainties in the observed photometry and the different epochs at which the optical and near-IR photometry were taken means that for most stars this correction of the IRTF and MILES spectra does result in perfect agreement in the overlap region. Since we are eventually going to stitch the two spectra together we need them to be at the same flux level, and any incongruity would affect the derived bolometric luminosities and spectral shapes around $0.7\mu m$. We force the MILES and IRTF spectra by computing the percent difference of the flux in the overlap region assuming that the IRTF spectra is at the correct level. Then, to ensure that we do not have flux going into the negative, if the difference is negative we shift the IRTF spectrum by that factor. If the difference is positive we shift the MILES spectrum by that factor.

In the case where 2MASS photometry is not available (e.g. HD 134439) but there is available near-IR photometry from Simbad we used the same basic method as described above but only considered the $K_{S}$-band photometry, using the raw difference between the observed and synthetic magnitudes. For variable stars in the sample, the absolute flux calibration is only approximate since the 2MASS photometry was obtained at an earlier epoch than the SpeX spectroscopy. However, consistency between the MILES spectra and IRTF spectra is a natural check of the calibration.

II.4.1 Quality of Flux Calibration

We assess the quality of the spectral shape of the IRTF spectra in Figure 10. Here we show a histogram of the error-normalized color differences between the observed and synthesized 2MASS (skrutskie2006) $J-H$ (left), $H-K_{S}$ (middle), and $J-K_{S}$ (right) colors. We also show in each panel of Figure 10 a Gaussian distribution of $\sigma=1$. Overall the differences between observed and synthesized colors are consistent with the errors in the observed colors. There is some tension in the $J-H$ and $H-K_{S}$ colors but not in $J-K_{S}$, suggesting that there might be some modest issue with the $H-$band normalization.

We further examine the quality of the flux calibration by computing the residuals between observed and synthetic photometric colors. For this exercise we choose stars with 2MASS photometry better than 3% for the $JHK_{S}$ bands and with good quality spectra and well-determined stellar parameters (see Table A and later for how we determine this); 124 stars in total. In Figure 11 we show these residuals as a function of effective temperature for the colors $H-K_{S}$ (upper-right), $J-K_{S}$ (lower-left), $B_{\rm T}-V_{\rm T}$ (we only display stars with Tycho photometry in this plot) and $V_{\rm T}-K_{S}$ (lower-right). The observed photometry have been redden corrected using the same $E(B-V)$ values used to correct the spectra. Points are color-coded by $J$ band magnitudes because at $J\sim 9$ and $J\sim 4.5$ the 2MASS observing strategy changed to avoid non-linearity and saturation for bright stars. This will affect the photometry and corresponding error bars.

For each color we find mean residuals of $0.022$, $-0.015$, $-0.026$, and $0.041$, respectively. The residuals for the near-IR colors are consistent with those of rayner2009 and the $B_{\rm T}-V_{\rm T}$ residuals are consistent with the result from sanchez2006. The $V_{\rm T}-K_{S}$ residuals are a reflection of the overall uncertainty of the absolute flux calibration and stitching of the MILES and IRTF spectra. Given the large wavelength baseline and the complications associated with stitching together different spectral datasets, it is not surprising that this color shows the largest offsets between synthesized and observed data.

We explore the reliability of the IRTF spectra further in Figure 12, where we compare our new IRTF spectra to the spectra in the rayner2009 IRTF library for four stars in common between the two libraries. In this figure we also compare to $BVJHK_{S}$ photometry and the MILES spectra. The bottom panel for each star shows the ratio between the old and new IRTF spectra. The agreement in the shape is excellent for HD076151 and HD036003, except at the blue end for the former where we see a small, unphysical bump in the flux at $\sim 0.8$ $\mu m$. This is caused by difficulty modeling the Paschen break in the A0 V standard and occurs in a small subset (4%) of our sample. We found that the stars showing this bump were flux calibrated with standard stars that show nebulosity (labelled A0 Vn in Simbad). This was not an issue in the rayner2009 library since the detectors did not extend to as blue wavelengths. This issue is addressed further in Section 3.

We explore the reliability of the flux calibration of the blue end of the SpeX spectra by comparing the Extended IRTF library stars with the Next Generation Spectral Library (NGSL gregg2001) which spans $1680$-$10000{\rm\AA}$. The NGSL spectra were observed on the STIS instrument on the Hubble Space Telescope (HST) so we can use these spectra as flux standards. There are 35 Extended IRTF Library stars that are also in NGSL. To measure how consistent the flux calibration of the Extended IRTF Library is with NGSL we synthesized SDSS $i$ and $z$ photometry (the two passbands that span the blue end of the Extended IRTF Library spectra) for both the NGSL and Extended IRTF Library spectra for the 35 overlap stars. In Figure 13 we show the residuals between the NGSL $i$-$z$ colors and the IRTF $i$-$z$ colors. The mean residual is sub-1% with a scatter on the order of a few percent, indicating consistency between the flux calibration of the NGSL spectra and the IRTF spectra.

The shape of the spectra is important for computing bolometric luminosities and in creating stellar population models. Consistency at the level of absorption lines between the old and new IRTF spectra is also important as that will change equivalent widths and affect the accuracy of fitting stellar features using these spectra. From Figure 12 we can see that the differences between the rayner2009 stellar features and the stellar features in the spectra from this work are 1-2%, much smaller than the over all shape and flux level differences.

In Figure 14 we show a small sample of stars in the library. They are ordered from cool (upper left corner) to hot (lower right corner). The reduced, redshift corrected, and absolutely flux-calibrated spectra for all the stars observed as part of the Extended IRTF library are available at the IRTF website http://irtfweb.ifa.hawaii.edu/~spex/IRTF_Spectral_Library/.

II.5. Combining the Extended IRTF Library with MILES

The wavelength solution for the SpeX data is not linear and so there is no constant $\Delta\lambda$ between pixels. In practice this means that the spectra for the different stars in the library are on different wavelength grids. The first step to combining the SpeX spectra with the MILES spectra is to put all the Extended IRTF Library stars on the same wavelength grid. We did this by finding the wavelength range shared by all the stars in the library, $\lambda_{\rm min}=0.713$ $\mu m$ and $\lambda_{\rm max}=2.559$ $\mu m$ with 7408 wavelength points (with spacing between the pixels as $\Delta\lambda=2.495{\rm\AA}$), and interpolated every spectrum onto that grid.

With the Extended IRTF Library spectra all on a uniform wavelength grid we combine them with the MILES spectra (where we have converted the MILES wavelengths from being in air to being in vacuum) as follows: for each star, we took the weighted average between the MILES and the Extended IRTF spectra between 0.713$\mu m$ and 0.743$\mu m$ using a linear ramp function. The Extended IRTF Library spectra between 0.713$\mu m$-0.743$\mu m$ were placed on the MILES wavelength grid. At 0.728$\mu m$ the blend is half MILES and half IRTF. The final, combined spectrum is a concatenation of the MILES spectrum at $\lambda\leq 0.713\mu m$, the blended section, and the IRTF spectrum at $\lambda\geq 0.743\mu m$.

II.6. Bolometric Luminosity

To compute the bolometric luminosity for each star we extended the combined MILES and IRTF spectrum to $0.03\mu{\rm m}$ and $20\mu{\rm m}$ using the C3K stellar grid, and integrated the extended spectrum to obtain the bolometric flux. For most of the stars we used parallax based distances to convert from bolometric flux to bolometric luminosity. For the cluster stars we used cluster distances as a proxy for distance to the star (for NGC 6791, grundahl2008; harris1996, 2010 edition, for the rest).

14 stars or 5% have neither parallaxes nor known distances and so the bolometric luminosity cannot be computed for them.

II.7. Resolution

The nominal resolution of the SpeX instrument is $R\sim 2000$. In this section we characterize the wavelength-dependent SpeX resolution, which is essential for using these spectra to model observational data. We also re-measure the MILES spectral resolution for comparison.

The spectral resolution of the MILES/IRTF data was measured by fitting theoretical stellar spectra to these data with the Prospector code. Briefly, for each wavelength regime of each star we calculate a posterior probability distribution for the line spread function (LSF) width and residual velocity, marginalized over the stellar parameters. The log-likelihood for the data given these parameters is calculated by simple $\chi^{2}$ between the data and the smoothed theoretical model. This model is constructed by tri-linear interpolation of a high resolution version of the C3K theoretical stellar library in the stellar parameters log Teff, log$g$, and [Fe/H], which is then smoothed to a fixed resolution in $\Delta\lambda$(FWHM $\rm\AA$) using fast Fourier transforms, and interpolated to the wavelength scale of the data after shifting in velocity. This smoothing assumes a gaussian LSF with rms width $\Delta\lambda/2.355$. To minimize template mismatch, the stellar parameters log$g$, log Teff, and [Fe/H] are allowed to vary from the prugniel2011 parameters within some tolerance. The velocity and instrumental resolution $\Delta\lambda$ (${\rm\AA}$) have uniform priors within some reasonable range for each segment. The residual velocities are consistent with zero. This posterior probability is then sampled using MCMC techniques, specifically the ensemble sampling algorithm (goodman2010; fm2013). The resulting maximum a-posteriori values are reported, corrected for the resolution of the theoretical library.

These fits are done separately for several wavelength regions of the spectrum of each star; the optical spectra are split into 6 regions each 400${\rm\AA}$ wide, while 6 regions in the IRTF spectra are defined around prominent spectral features and avoiding regions of low atmospheric transmission.

In Figure 15 we show the median resolution (solid line) for 135 warm ($3980K<T_{\rm eff}<6300$K) stars and the scatter (shaded region) over twelve wavelength segments spanning the full Extended IRTF spectra. In the top panel we show the wavelength segments for the part of wavelength space covered by the MILES spectra and in the bottom panel we show the wavelength segments for the wavelength space covered by the IRTF spectra. In the top panel we show a constant line at $\Delta\lambda=2.54{\rm(\AA)}$, the revised resolution found by beifiori2011. The median resolution we find over the different wavelength regions of the MILES spectra is $\Delta\lambda=2.54{\rm(\AA)}\pm 0.19$ (R $\sim 1970$ at 0.5$\mu m$), consistent with the beifiori2011 value. In the bottom panel we show a constant line for $R\equiv\lambda/\Delta\lambda=2000$. The median resolution we find over the different wavelength regions for the IRTF spectra is $R=2020\pm 230$, consistent with the quoted value for the SpeX instrument.

III. Spectral Polynomial Interpolator

Interpolators have long been used in conjunction with stellar libraries. What began as “fitting functions” for specific indices (e.g., gorgas1993; worthey1994) has now evolved to full spectral interpolators (e.g., vazdekis2003; prugniel2011; ness2015; sharma2016; dries2016). Broadly, interpolators are either “global”, where a polynomial is fit to the input sample points, or “local”, which essentially averages the nearby data e.g., the linear or spline interpolation is a weighted average of only the data closest in parameter space. Global interpolation is appropriate when the surface is smooth and can be approximated by a (relatively) simple function. The interpolators of vazdekis2003 and dries2016 are local interpolators while the interpolators described in prugniel2011, ness2015, and sharma2016 are global.

In this same spirit, as a companion to the Extended IRTF library we created the Spectral Polynomial Interpolator (SPI 333http://github.com/bd-j/spi). With SPI we create a data-driven, global interpolator which we can use to retrieve a spectrum for a set of arbitrary stellar parameters. In this section we will describe the input to SPI, how we construct the model, the quality of interpolation, and example uses for SPI.

III.1. The Training Set

SPI works by fitting polynomial functions of $T_{\rm eff}$, log$g$, and [Fe/H] to the $L_{\rm bol}$-normalized flux of all the stars included in the training set. These fits are carried out independently of the fluxes at each wavelength. Then, for any set of stellar parameters, these polynomial functions can be used to predict or approximate the flux at a given wavelength.

The primary input into SPI is the IRTF Extended Library, limiting the sample to stars with computed bolometric luminosities (see section 2.4.1), high-quality spectra, and accurate stellar parameters (more on the latter two later; see also Table A). The library stars that made the final cut to be included in the training set are shown as red points in Figure 16. We have augmented the SPI training set in a couple of ways, which we describe below. In total 194 Extended IRTF Library stars were included in the final SPI training set.

We include the wavelength dependent uncertainties for every star in the training set and weight the fluxes in the training sample by the corresponding uncertainty.

III.1.1 Additions to the Cool Dwarf Regime

We can see from Figure 1 that there is a paucity of cool dwarf stars in the MILES library and subsequently the library presented in this work. Having few cool dwarf stars would have hindered our ability to build an accurate polynomial model in this regime. We therefore included 76 M dwarf stars presented in mann2015 to the SPI training set (purple points in Figure 16), excluding stars with low SNR. We also found that 4 stars had strong chromospheric Balmer emission lines which we removed from the training set.

The spectra from mann2015 are a combination of SNIFS ($0.3-0.95\mu m$) and pre-detector upgrade SpeX ($0.8-2.4\mu m$). The resolution of the SNIFS data is coarser (R$\sim 1000$) than the resolution of the MILES data. To put the SNIFS data on the same spectral resolution scale as the MILES data we used a high resolution (R$\sim$10,000) version of C3K to deconvolve the SNIFS portion of the mann2015 data to the resolution of the MILES data. We did this by producing a spectrum using the stellar parameters of a given star in the mann2015 sample and made two models, one each for the MILES and SNIFS resolutions. We took the ratio of these two models, interpolated it onto the MILES wavelength grid and multiplied the mann2015 spectrum by this correction factor. Visual comparison of a SNIFS and MILES star of the same stellar parameters led us to conclude that this procedure was effective.

We use the stellar parameters as presented in mann2015 with surface gravity given by,

[TABLE]

where $M$ and $R$ represent the stellar mass and radius in solar units.

We note that while we use surface gravity to make the parameterization of the M dwarf stars consistent with the other regimes, surface gravity is not a commonly used metric in M dwarf research. M dwarfs do not age on a Hubble time and so surface gravity can be uniquely determined by effective temperature and metallicity.

III.1.2 Support for extrapolation

To preserve the quality of the interpolator at the edges of the empirical parameter space, we supplement the training set with spectra from the theoretical C3K library (grey points in Figure 16) degraded to the SpeX resolution. We only added C3K spectra for stellar parameters outside the convex hull (a hull being the set of planes that encloses all the training points) of the MILES stars. The C3K spectra are normalized in the same way as the observed spectra.

Our goal is for the C3K library to keep the polynomial terms “well-behaved” at the boundaries of parameter space for the empirical spectra, but we do not want the fits to be driven by the large numbers of C3K stars. We therefore weight the C3K spectra in the fits by a factor of $10^{-2}$ times the median SNR of the empirical spectra. This factor was chosen after considering a range of values and inspecting the resulting polynomial behavior.

III.2. Training the Model

The library contains a wide range of spectral types, with stellar temperature being the primary driver of the shape of the spectra. Modeling all the stars together is not feasible since it is difficult to specify a polynomial model that can encompass such a diverse set of stars. We therefore partition the library into five subsets based on temperature and surface gravity, essentially making five global interpolators that we use in conjunction with each other to span the entirety of parameter space. For each subset we define the polynomial terms we use to create the model ($t\equiv{\rm log}\,T_{\rm eff}$, $z\equiv$[Fe/H], $g\equiv{\rm log}\,g$):

• •

Cool Dwarfs

[TABLE]

• •

Cool Giants

[TABLE]

• •

Warm Dwarfs

[TABLE]

• •

Warm Giants

[TABLE]

• •

Hot Stars

[TABLE]

The maximum likelihood coefficients for each regime are determined by weighted linear least squares. The glut of polynomial terms is a classic problem in polynomial regression modeling. As we are concerned with the ability to predict spectra (which we assess later in Section LABEL:spi_quality) rather than the values of the coefficients themselves we do not make an effort to simplify the polynomial functions using, e.g., L1 regularization. Furthermore, the oscillatory behavior of extrapolations that can result from unregularized high order polynomial regression is mitigated by our use of theoretical spectra near the boundaries of the valid parameter space.

In Table III.2 we show the “training” ranges for $T_{\rm eff}$, log$g$, and [Fe/H], i.e., the stellar parameter limits for the training set stars in each regime and the “Interpolating” ranges for $T_{\rm eff}$, log$g$, and [Fe/H], i.e., the stellar parameter limits for safe interpolation. We have the same range in metallicity for the training bounds of all the stellar regimes. The ranges were determined by minimizing the rms difference between the observed and interpolated spectra in the training set. The overlap in the $T_{\rm eff}$ training ranges is meant to mitigate the effect of five separate, disjoint hulls having a smaller volume than the hull for all the library points. For most regimes the overlap in Teff is 500 K but for the cool dwarf regime we extend the training sample to 5500 K. We do this to compensate for the paucity of low-metallicity cool dwarfs in the empirical library. If we did not extend the training sample to 5500 K the metallicity dependence for the cool dwarf regime would end at [Fe/H] $\sim$ -0.7, which would bias the interpolation to lower metallicities. With the extended temperature range of the training sample SPI is able to pull information from the warmer low-metallicity stars which mitigates the effects of the lack of observed low-metallicity cool dwarfs.