Strömgren and Hb photometry of stars in dark clouds

May 25, 2007

Dan Piehl
University of Wisconsin-Oshkosh
Graduate Student Independent Study

1.  Introduction

In their survey of eight Bok Globules, Sen et al. 2000 included tables of polarization data for these stars. Much of this data was used in the analysis of magnetic fields existing in these dark clouds.

This independent study will attempt to utilize photometric techniques and answer some questions as to the distances to the clouds, using Strömgren and Hb photometric systems.

2.  Observing program

The observations consist of FITS-formatted CCD frames provided by Dr. Briley at UW-Oshkosh, observed during five nights starting October 30, 2005 at KPNO. The telescope was equipped with a 2048 ´ 2048 pixel CCD camera. This resolution corresponds to about 1.7" per pixel. The CCD detector was maintained with a dewar cooled to -166 C. For this program, six filters were used. On a filter wheel, the telescope imagery is sampled in each of the four-color Strömgren uvby bands, as well as Hb wide and narrow bands.

This filter arrangement enables measurement of V (the visible magnitude parameter) and b-y (the color index). Additionally, c₁ = (u-v) - (v-b) measures the Balmer decrement, and m₁ = (v-b) - (b-y) measures line absorption effects. The value b examines a narrowband region centered at the H_b hydrogen line. Due to additive effects of errors in each of the three-filter derived index values, c₁ and m₁, it is particularly challenging to achieve small errors in those values. For that reason, many of the fainter stars in this examination will not have measurements of those index values. To minimize this error, the transformation solutions take place on these derived values themselves, rather than solving for coefficients each filter separately.

The standard stars were chosen from the lists of Stetson (1991) and Hauck & Mermilliod (1998). Dome flats were acquired each night, so that CCD images can be corrected for scalar differences between pixels. It is common that there is illumination nonuniformity of the CCD sensor during acquisition of these dome flats. Therefore, a set of sky flats is taken, with the telescope directed at a small region of twilight sky. Combined together between different nights, these sky flats can suppress large-scale illumination errors. Together, these flats (and subtraction of bias frames) are handled by IRAF (Imaged Reduction and analysis facility) software during the flatfielding process.

The targeted program stars consist of selected field stars in dark clouds CB3, CB25, CB39, CB52, CB54 (parts A and B), CB246, and the extended regions CB3N and CB25N as identified by Sen et. al. (2000) for which the polarimetry has been examined. Some insight into other physical parameters might explain more about the dark clouds. In determining these photometric values, all five nights are used. But there is reliance on only one photometric night, making a system of secondary standards necessary. Ten secondary standard stars in each program frame were assigned for the purposes of solving transformational parameters for frames acquired on non-photometric nights. These secondary standards are essential to account for the extinction and color transformational differences that can vary from one frame to the next during the same night.

3.  Observations and Data Reduction

3.1.  Initial reductions

These reductions using IRAF include overscan correction, zero-frame subtraction, and flatfielding. The zero (or bias) frames and the flats are combined using IRAF's imcombine task. The dome flats were divided by the sky flats, and were heavily smoothed using IRAF's mkillumcor task, making illumination correction frames for each night. During flatfielding, this permits IRAF ccdproc to correct illumination gradients.

3.2.  Aperture photometry

Following flat field corrections, the instrumental magnitudes were computed using an aperture photometry routine, phot, which subtracts the sky background flux measured near each star. The conversion of instrumental magnitudes to the uvbyb  system was carried out using a parameter fitting routine in IRAF against the primary standards, followed by an inverse transformation of both the program stars and the secondary standards identified on every frame. This process was then repeated on non-photometric nights, using the secondary standards.

A choice was made to use a sky annulus with inner radius 18 pixels and a width of 10. An aperture size of 12 pixels was used. This amounts to about 4 times the FWHM of the flux distribution of the stars observed. While some authors recommend a smaller aperture, closer to r » FWHM (Mighell 1991), there were concerns that this would not capture all of the measurable flux from the star, possibly causing problems with frames having poor tracking or less than ideal seeing conditions. The choice to use a larger aperture is made at the expense of photometric error due to the presence of more sky pixels consisting of background flux. In principle, the choice of a larger aperture should lead to more uniformity of flux acquisition from night-to-night. This permits exclusion of strongly variable stars and stars whose faint magnitudes cannot be reproducibly discerned. To aid in excluding the unreliable data, a rejection of photometric data deviating by more than 2s among all the nights was utilized.

3.3.  Transformations to the standard systems

The quantity V generally scales with the y filter. However, the V-magnitude includes a color-dependent term, while the y-magnitude is nearly monochromatic. This heterochromatic value can be derived by noting that the two magnitudes coincide when b-y is around 0.55. Therefore, this departure can be approximated using a squared term in b-y, as outlined by Budding (1993). After discovering this nonlinear dependency in the parameter fitting, the squared term, 0.12[(b-y)-0.55]² was included in the transformation equations.

During the process of solving the equations, the standard stars were given equal weights. Using subscripted X values to represent computed airmass quantities for each filter, the transformation equations are designed to map standard star photometric indices into instrumental system. IRAF will iteratively solve for coefficients, and the choice was made set a rejection of stars whose residuals deviate from the fit by more than 2s.

The solved transformation equations are:

yi =	5.356	+0.136	Xy	+0.117	(b-y)	+	V	+0.12 [(b-y)-0.55]2	s = 0.0093
	±13	±10		±6
(b-y)i =	0.061	+0.057	Xb	+0.942	(b-y)				s = 0.0082
	±11	±9		±6
mi =	0.108	+0.070	Xv	+0.110	(b-y)	+1.249	m1		s = 0.0128
	±17	±13		±17		±51
ci =	0.470	+0.114	Xu	-0.189	(b-y)	+0.998	c1		s = 0.0104
	±16	±10		±10		±7
bi =	-0.058	+1.033	b						s = 0.0083
	±33	±12

Note that the arrangement of terms is reversed from Crawford (1970), in that the instrumental terms appear on the left. This format is helpful in that IRAF will solve for airmass coefficients and color transformational coefficients at the same time. It is then possible, using the system's inverse transformation that IRAF derives with the invertfit task, to find corresponding values within the standard system for night 3's program stars.

Using the set of ten secondary standards selected in each frame, this process was repeated using the secondary standard values for each of the corresponding frames on the non-photometric nights. However, the airmass term is eliminated from this secondary transformation process, since it can be absorbed into the constant term. This is possible because there is no significant airmass variation between the secondary standards and the desired program stars (they are on the same frame). So the airmass term is redundant and only makes fitparams unstable when resolving which term serves as the constant photometric difference between frames from photometric and non-photometric nights.

4.  Results and Discussion

The measured photometric magnitudes are presented in Tables 1 through 9.

Table 1. Observed photometry for field stars in CB3

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	12.999	0.006	0.304	0.010	0.129	0.025	0.812	0.035	2.795	0.025
2	16.935	0.079	0.517	0.228
3	16.398	0.339	0.761	0.167	0.292	0.088
4	16.791	0.078	0.785	0.068	0.111	0.195			2.564	0.038
5	14.661	0.032	0.489	0.076	0.004	0.113	0.520	0.057	2.618	0.107
6	12.051	0.009	0.374	0.012	0.094	0.014	0.510	0.025	2.683	0.009
7	14.129	0.005	0.479	0.020	0.102	0.090	0.404	0.087	2.626	0.034
8	15.394	0.215
9	13.151	0.012	0.444	0.018	0.087	0.021	0.446	0.025	2.643	0.023
10	17.364	0.201	0.685	0.164
11	14.946	0.023	0.627	0.029					2.799	0.117
12	15.373	0.023	0.580	0.029					2.565	0.131
13	17.581	0.248
14	16.953	0.047	0.636	0.060	0.116	0.290			2.568	0.217
15	14.767	0.037	0.607	0.076	0.069	0.089	0.330	0.164	2.662	0.134
16	15.630	0.031	0.585	0.048	0.132	0.442	0.513	0.260	2.617	0.175
17	15.818	0.044	0.558	0.113	0.036	0.230	0.536	0.110	2.480	0.320
18	14.141	0.011	1.033	0.025	0.244	0.085	0.329	0.267	2.566	0.056
19	14.433	0.138	0.416	0.019	-0.040	0.043	1.118	0.283	2.990	0.101
20	14.487	0.024	0.456	0.038	0.066	0.103	0.907	0.303	2.845	0.024
21	13.962	0.021	0.545	0.015	0.164	0.120	0.399	0.057	2.552	0.036
22	17.230	0.146
23	16.945	0.112	0.579	0.258
24	15.423	0.018	0.479	0.104	0.186	0.257	0.617	0.254	2.557	0.158
25	15.279	0.033	0.629	0.059	-0.105	0.102			2.802	0.101
26	14.376	0.012	0.498	0.015	0.141	0.054	0.262	0.250	2.617	0.122
27	14.398	0.019	0.505	0.029	0.112	0.047	0.485	0.077	2.650	0.057
28	13.948	0.011	0.390	0.017	0.057	0.108	0.655	0.053	2.699	0.005
29	15.815	0.019	0.532	0.099	0.173	0.196	0.361	0.258	2.589	0.105
30	14.825	0.008	0.506	0.032	0.146	0.157	0.381	0.143	2.541	0.051
31									2.833	0.022

Table 2. Observed photometry for field stars in CB25

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	15.509	0.021	0.858	0.112	-0.182	0.083	0.739	0.043	2.618	0.077
2	16.645	0.182	1.254	0.269					2.744
3	16.593	0.152	0.991	0.147					2.680	0.259
4	15.208	0.061	0.774	0.032	0.484	0.117			2.481	0.164
5	16.845	0.054	0.915	0.215
6	16.835	0.057	0.850	0.335
7	17.286	0.134	1.175	0.132
8	15.953	0.172	0.719	0.039	0.056	0.189	0.768	0.226	2.769	0.130
9	13.963	0.014	1.349	0.059					2.589	0.026
10	17.120	0.204	1.083	0.343					2.775
11	15.079	0.078	0.928	0.073	0.045	0.212	0.373	0.055	2.698	0.099
12	17.189	0.150	0.576	0.416					2.432
13	16.897	0.140	1.467	0.150					2.540
14	17.015	0.054	0.886	0.021
15	15.288	0.031	1.204	0.088					2.637	0.208
16	17.378	0.364	1.011	0.071					2.651
17	17.605	0.150	0.881	0.186
18	17.447	0.035	0.776	0.141
19	16.067	0.189	1.062	0.226
20	17.422	0.059	1.378	0.334					2.877
21	18.404		0.310

Table 3. Observed photometry for field stars in CB39

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	17.563	0.423
2	17.308	0.436
3	15.174	0.214	1.359	0.346
4	16.630	0.270	0.887	0.413
5	15.916	0.192	0.734	0.441
6	17.528	0.344
7	16.961	0.190							2.570	0.183
8	17.616	0.470
9	14.710	0.179	1.176	0.312
10									2.488	0.100
11	16.828	0.253	0.649	0.182	-0.087	0.441
12
13	14.035	0.173	0.578	0.401	0.259	0.109	0.469	0.463	2.499	0.249
14	15.907	0.084	1.063	0.189					2.850
15	17.029	0.204
16	14.263	0.167	0.650	0.422	0.191	0.108			2.522	0.268
17	16.050	0.214
18	16.051	0.261	1.079	0.323	-0.089	0.230			2.549	0.218
19
20	14.043	0.226	0.585	0.410	0.108	0.084	1.183	0.420	2.794	0.237
21	15.021	0.193	0.894	0.396

Table 4. Observed photometry for field stars in CB52

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	12.924	0.010	0.417	0.003	0.120	0.004	0.379		2.556
2	17.705	0.193
3	15.990	0.053	0.773	0.051	0.488	0.050			2.755
4	16.399	0.077	0.816	0.074					2.964
5	17.607	0.188
6	14.415	0.003	0.420	0.011	0.154	0.012	0.275	0.002	2.635
7	13.315	0.015	0.449	0.003	-0.054	0.005	0.878		2.820
8	16.585	0.108
9
10	14.396	0.007	0.500	0.010	0.183	0.012	0.171	0.001	2.586
11	16.726	0.117
12
13
14	15.840	0.079
15
16	17.537	0.205

Table 5. Observed photometry for field stars in CB54A

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	12.224	0.014	0.480	0.018	0.287	0.037	0.332	0.047	2.633	0.010
2	11.911	0.015	0.331	0.008	0.131	0.047	0.383	0.015	2.616	0.013
3	13.017	0.015	0.300	0.013	0.149	0.052	0.427	0.007	2.685	0.004
4	15.996	0.150	0.788	0.030					2.152	0.029
5	15.476	0.099	0.625	0.122	0.301				2.723
6	15.182	0.053	0.388	0.013	-0.008	0.034			2.571	0.221
7	15.008	0.076	0.616	0.113	0.089	0.462			2.642	0.028
8	16.606	0.187	1.005	0.281					2.301
9	15.077	0.044	1.011	0.035	0.061		0.157		2.676	0.050
10	15.363	0.014	0.488	0.004	0.053	0.037	0.987	0.141	2.898	0.009
11	16.844	0.267	0.520	0.338					3.017
12	13.740	0.004	0.377	0.009	0.139	0.006	0.353	0.093	2.585	0.015
13	16.110	0.178	0.870	0.124	0.144				2.698
14	15.925	0.025	0.998	0.021
15	15.529	0.042	0.688	0.118	-0.018	0.319			2.668	0.014
16	16.992	0.042	0.589	0.092					2.372
17	15.086	0.029	0.630	0.001	-0.010	0.037	0.364		2.571	0.035
18	16.812	0.262	1.011	0.411					2.599
19	17.051	0.095	0.327	0.287					2.762
20	16.375		0.996
21	17.871		0.133
22	13.062	0.022	0.160	0.018	0.126	0.046	0.980	0.004	2.898	0.037
23	17.004		0.533						2.633
24	18.123		0.117
25	16.338	0.027	0.592	0.119
26	15.756		0.337		0.249				2.426
27	13.527	0.035	0.438	0.016	0.076	0.016	0.483	0.122	2.607	0.007

Table 6. Observed photometry for field stars in CB54B

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	14.763	0.009	0.577	0.025	0.116	0.136	0.350	0.033	2.664	0.034
2	11.675	0.018	1.175	0.038	0.567	0.045	0.096	0.138	2.559	0.008
3	15.650		1.145						2.534	0.048
4	14.712	0.066	0.505	0.043	0.399	0.335			2.602	0.176
5	16.619	0.288	0.485	0.206	-0.140
6	14.834	0.052	0.523	0.001	0.079	0.103	0.683	0.231	2.673
7	13.213	0.022	0.314	0.009	0.144	0.013	0.422	0.125	2.632	0.005
8	15.973	0.016	0.598	0.042	0.108		0.773		2.408
9	14.420	0.015	0.579	0.013	0.094	0.075	0.569	0.008	2.621	0.089
10	15.898	0.109	0.402	0.048	-0.123	0.057			3.016	0.355
11	15.436	0.033	0.461	0.014	0.058	0.132			2.695	0.145
12	15.032	0.036	0.417	0.061	0.066	0.033	0.686	0.081	2.798	0.185
13	14.296		0.433		0.097		0.441		2.650
14	16.812	0.173	0.225	0.366					2.762
15	14.690	0.024	0.377	0.013	0.113	0.047	0.472	0.086	2.619	0.029
16	13.834	0.029	0.414	0.032	0.242	0.044	0.330	0.018	2.590	0.041
17	14.434	0.020	0.389	0.008	0.163	0.081	0.390	0.349	2.680	0.118
18	16.191	0.103	0.550	0.344	-0.051	0.117	0.599		2.402	0.127
19	16.526	0.016	0.509	0.132					2.414	0.011
20	12.853	0.009	0.285	0.001	0.185	0.002	0.711	0.100	2.784	0.013
21	12.224	0.014	0.480	0.018	0.287	0.037	0.332	0.047	2.633	0.010

Table 7. Observed photometry for field stars in CB246

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	12.100	0.015	0.453	0.023	0.197	0.023	0.332	0.033	2.584	0.011
2	17.032	0.176							2.628	0.202
3	13.106	0.009	0.522	0.024	0.256	0.040	0.316	0.082	2.594	0.030
4	18.448		0.623
5	17.195	0.059	1.010	0.210					2.497	0.066
6	15.866	0.225	1.025	0.226	-0.105	0.346			2.644	0.222
7	17.251	0.310	0.915	0.279	-0.076
8
9	16.063	0.104	0.769	0.076	-0.039	0.148
10	16.464	0.315	1.358	0.071					2.179	0.073
11
12	16.879	0.125
13	16.266	0.152	1.189	0.235
14	16.334	0.210	1.292	0.415

Table 8. Observed photometry for field stars in CB3N

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	15.689	0.115	0.494	0.061					2.645	0.158
2	14.807	0.016	0.847	0.041	0.258	0.172	0.342	0.406	2.576	0.094
3	15.561	0.038	0.438	0.034	0.018	0.068			2.636	0.127
4	15.757	0.019	0.516	0.033	0.094	0.092	0.499	0.164	2.637	0.088
5	15.228	0.027	0.747	0.056	0.306	0.141	0.284	0.147	2.595	0.172
6	15.972	0.098	0.561	0.083	-0.045	0.236	0.483	0.335
7	14.652	0.008	0.436	0.049	0.121	0.107	0.600	0.125	2.727	0.051
8	15.646	0.030	0.486	0.030	0.094	0.109	0.504	0.094	2.721	0.189
9	14.436	0.015	0.352	0.008	0.132	0.033	0.692	0.231	2.827	0.089
10	14.345	0.012	0.562	0.018	0.126	0.094	0.405	0.094	2.599	0.043
11	17.293	0.455	0.325	0.261	0.133	0.359	0.633	0.418
12	16.562	0.199	0.479	0.182	-0.044	0.418
13	15.607	0.067	0.456	0.050	0.034	0.046	0.764	0.130	2.709	0.106
14	14.581	0.027	0.443	0.046	0.025	0.263	0.638	0.118	2.720	0.111
15									2.637	0.049
16	15.751	0.024	0.597	0.027	0.143	0.092	0.189	0.153
17	15.907	0.150	0.961	0.264	0.472	0.215	0.616
18	14.808	0.031	0.554	0.034	0.114	0.103	0.489	0.173	2.605	0.050
19	16.894	0.203	0.723	0.152					3.071	0.001
20	15.319	0.145							2.560	0.108
21	16.792	0.099	0.484	0.265	0.283	0.141	0.406
22	15.710	0.045	0.667	0.183					2.375	0.129
23	14.981	0.058	0.430	0.037	0.106	0.119	0.618	0.124	2.644	0.122
24	17.705	0.154	0.328	0.186	0.311	0.284			2.688	0.110
25	13.831	0.024	0.849	0.020	0.280	0.027	0.237	0.143	2.558	0.035
26	16.189	0.102	0.683	0.433	0.262	0.350	0.294	0.330	2.676	0.206
27	13.964	0.018	0.512	0.030	0.031	0.046	0.465	0.055	2.618	0.053
28	12.999	0.006	0.304	0.010	0.129	0.025	0.812	0.035	2.795	0.025
29	14.466	0.018			0.200	0.062	0.381	0.103
30	14.522	0.060	0.488	0.049	0.207	0.144	0.725	0.434	2.579	0.125
31	16.935	0.079	0.517	0.228	-0.016	0.301	0.399	0.313
32	14.661	0.032	0.489	0.076	0.004	0.113	0.520	0.057	2.618	0.107
33	13.151	0.012	0.444	0.018	0.087	0.021	0.446	0.025	2.643	0.023

Table 9. Observed photometry for field stars in CB25N

Sr.#	V	E(V)	b-y	E(b-y)	m1	E(m1)	c1	E(c1)	b	E(b)
1	16.562	0.247							2.772	0.093
2	17.244	0.122	1.073	0.059
3	15.225	0.037	1.067	0.063					2.580	0.123
4	13.544	0.020	0.847	0.050	-0.051	0.118	0.826	0.211	2.780	0.073
5	12.333	0.012	0.523	0.020	0.177	0.040	0.329	0.063	2.633	0.028
6	16.690	0.412
7	16.941	0.050	0.584	0.044					2.783	0.141
8
9	17.342	0.329
10	17.269	0.208
11	17.731	0.452
12
13	14.605	0.056	0.776	0.065	-0.107	0.133	1.202	0.103	2.916	0.042
14	16.193	0.086	0.469	0.213	0.112	0.158
15	15.585	0.079	1.084	0.117					2.630	0.033
16	15.509	0.021	0.858	0.112	-0.182	0.083	0.739	0.043	2.618	0.077
17	16.585	0.143	0.994	0.145	0.175				2.497
18	16.761	0.302

Using gnuplot, a computer program that can generate plots of data, we can examine the m₁ and c₁ indices relative to the b-y index.

Fig. 2. Plot of b-y vs. m₁

Fig. 3. Plot of b-y vs. c₁

These plots are not corrected for interstellar reddening. So some corrections must be made. The "bracketed" indices, [m₁] and [c₁], which are compensated for reddening using a b-y term, can be plotted against each other, making possible classification of spectral types (Strömgren 1966). The following relations are needed:

	[m1]	= m1	+ 0.32 (b-y)
	[c1]	= c1	- 0.20 (b-y)

Because of the reddening effects, it is helpful to plot the positions in the [m₁],[c₁] diagram and compare them to main-sequence data . The solid curve in the plot is the main-sequence using indices unaffected by reddening.

Fig. 4. An [m₁],[c₁] diagram, showing estimates of reddening-free physical parameters

In Fig. 4., the plot seems to indicate an abundance of A and F type stars. Another approach is to plot the data using the b index. This value is derived from spectrally concentric filters, so it is unaffected by interstellar reddening.

Fig. 5. Plot of b vs. b-y

The plot shows stars in CB25/CB25N are most affected by reddening. This coincides with the findings of Sen et. al (2005) that CB25 is more strongly polarized (3.32%) than the other clouds.

Fig. 6. Plot of b vs. V

5. Conclusions

Photometric data has been presented for regions of selected Bok Globules. Use of this data is appropriate for determining the distances of these dark clouds. This process for A and F type stars in dark clouds has been carried out by Franco (1988).

References	Web Links
Sen A., Gupta R., Ramaprakash A., Tandon S., 2000, A&AS 175	PDF
Hauck B., Mermilliod M., 1998, A&AS 129, 143	Catalogue
Strömgren B., 1966, ARA&A, p. 433	PDF
Crawford, D., Barnes J., 1970, AJ 75, 822
Budding E., 1993, An Introduction to Astronomical Photometry, p. 76, 77
Larsen S., 1996, Field star populations in the Magellanic Clouds	Postscript
Kaltcheva N., Olsen E., 1999, A&A, p. 600	PDF
Stetson P., 1991, AJ, August 1991 p. 589	Abstract
Mighell K., 1999, in "CCD Aperture Photometry", ASP Conf. Ser., Vol. 189, p. 50
Massey P., Davis L., 1997, in "A User's Guide to Stellar CCD Photometry with IRAF"	PDF
Franco, G., 1988, A&A 200, p. 173	Abstract
Sen A., Mukai T., Gupta R., Das H., 2005, MNRAS 361, 177	Abstract