-
Notifications
You must be signed in to change notification settings - Fork 0
/
Light_Curve_Fit.py
1337 lines (1053 loc) · 48.5 KB
/
Light_Curve_Fit.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jan 6 15:39:09 2021
Last Edit: Tues Mar 2 13:29:54 2021
@author: luciescharre/euannewlands
Description: This code reads in time-scaled catalogs from WASP-2 (WASAP-2b transit) observation.
WASP-2 and 3 comparison field stars are used read in. Atmospheric effects are corrected for by using the field stars
where the final corrected WASP-2 flux is plotted and a light curve is fitted using the batman package.
The best fit light curve is determined and the model returns best fit parameters, used to determine the properties of WASP-2b
"""
import os
import matplotlib.pyplot as plt
from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,
AutoMinorLocator)
import numpy as np
import batman
import scipy.optimize as spicy
from scipy.stats import chisquare
def chsq(oflux,eflux,ferr,params): # arrays of both
chisq=np.sum(((oflux-eflux)**2)/ferr**2)
#pchisq=np.sum(((oflux-eflux)**2)/eflux**2)
#print(chisq,len(oflux))
#print(pchisq)
rchisq=chisq/(len(oflux)-len(params))
print("reduced chi-square = %s"%rchisq)
return rchisq
def rJup(rstar,rerr):
conv=0.10045 # jupiter radii in solar radii
R_coll=0.79 # wasp2 radii in solar radii (Collier et al. 2006)
R_add=0.866 # wasp2 radii in solar radii (Addison et al. 2019)
rj=rstar*R_coll/conv
rjerr=rj*(rerr/rstar)
return rj,rjerr
def div_err(v1,v2,e1,e2):
# v1 is the numerator, v2 is the denominator, e1/e2 are corresponding errors
pe1=e1/v1
pe2=e2/v2
p_err=np.sqrt(pe1**2 + pe2**2) # adding percentage errors in quadrature
err=(v1/v2)*p_err
#print(e1[5],v1[5],pe1[5],pe2[5],p_err[5],v1[5]/v2[5],err[5])
return err
def w_mean(c1,c2,c3,e1,e2,e3): # weighted mean of flux fluctuations from independent measurements
vals=[c1,c2,c3]
es=[e1,e2,e3]
ws=[0,0,0]
s1=[0,0,0]
for i in range(3):
ws[i]=1/(es[i]**2) # smaller the error, the greater the weight
s1[i]=vals[i]*ws[i] # multiplying value by weight
S1=sum(s1)
S2=sum(ws)
mean=S1/S2 # values with greater weight count more
merr=np.sqrt(1/S2)
#print(c1[0],e1[0],mean[0],merr[0])
return mean,merr
def scaleError(ferr,scale):
s_err=ferr*(1/scale) # an array of errors scaled by the same factor
return s_err
def etest(of,ef,err):
count=0
for i in range(len(of)):
if ((of[i]+err[i]>=ef[i]) and of[i]<=ef[i]) or (of[i]-err[i]<=ef[i] and of[i]>=ef[i]):
count+=1
frac=count/len(of)
if frac<(2/3): # if fraction if less than 2/3 increase error bar size
up=True
else:
up=False
return frac,up
def scale_err(nWFlux,MFlux,errs):
# find the optimum scale to find 2/3 of error bars to cross
scalar=4.5
s_err=scaleError(errs,scalar)
no=0.
while no < 0.661 or no > 0.661: # finds scale for error bars such that 2/3 cross model curve
print('Scalar value is %s' %scalar)
s_err=scaleError(errs,scalar)
no,up=etest(nWFlux,MFlux,s_err)
print(no)
#print(no,up)
if no > 0.661 and no < 0.671:
print('Final scalar value is %s' %scalar)
break
if up==True:
scalar-=0.001
if up==False:
scalar+=0.001
return s_err
def read():
NUMBER =[]
FLUX_APER = []
FLUXERR_APER = []
MAG_APER = []
MAGERR_APER = []
X_IMAGE = []
Y_IMAGE = []
NUMBER_C1 =[]
FLUX_APER_C1 = []
FLUXERR_APER_C1 = []
MAG_APER_C1 = []
MAGERR_APER_C1 = []
X_IMAGE_C1 = []
Y_IMAGE_C1 = []
NUMBER_C2 =[]
FLUX_APER_C2 = []
FLUXERR_APER_C2 = []
MAG_APER_C2 = []
MAGERR_APER_C2 = []
X_IMAGE_C2 = []
Y_IMAGE_C2 = []
NUMBER_C3 =[]
FLUX_APER_C3 = []
FLUXERR_APER_C3 = []
MAG_APER_C3 = []
MAGERR_APER_C3 = []
X_IMAGE_C3 = []
Y_IMAGE_C3 = []
NUMBER_C4 =[]
FLUX_APER_C4 = []
FLUXERR_APER_C4 = []
MAG_APER_C4 = []
MAGERR_APER_C4 = []
X_IMAGE_C4 = []
Y_IMAGE_C4 = []
# read in catalog
cata='w2b'
#cata=str(input('catalog: '))
# catalog choices depending on data reduction
if cata == '1':
catadata='catalogs'
tfile='WASP.txt'
elif cata=='2':
catadata='catalogs2'
tfile='WASP.txt'
elif cata=='3':
catadata='catalogs3'
tfile='WASP.txt'
elif cata=='lit':
catadata='catalogsL'
tfile='WASP_Maybe.txt'
elif cata=='GV':
catadata='catalogsGV'
tfile='WASP_Maybe.txt'
elif cata=='mb':
catadata='catalogs3_MAYBE'
tfile='WASP_Maybe.txt'
elif cata=='GVf':
catadata='catalogs_20pix_GV'
tfile='WASP_Maybe.txt'
elif cata=='Lf':
catadata='catalogs_20pix_L'
tfile='WASP_Maybe.txt'
elif cata=='w2b':
catadata='wasp2b_transit'
tfile='time.txt'
entries = os.listdir('/Users/Euan/Desktop/LC_LS/%s'%catadata) #adjust this to your path
entries.sort()
for filename in entries:
if filename.endswith('.cat'):
with open(os.path.join('/Users/Euan/Desktop/LC_LS/%s'%catadata, filename)) as filein:
#content = filein.read()
for line in filein.readlines(): #iterates through the lines in the file
if not line.startswith('#'):
tokens = line.split() # breaks line into tokens seperated by ,
#WASP 2
#after telescope flip
#before telescope flip
if 856<=float(tokens[5])<=861:
if 1036<=float(tokens[6])<=1040:
NUMBER.append(float(tokens[0]))
FLUX_APER.append(float(tokens[1]))
FLUXERR_APER.append(float(tokens[2]))
MAG_APER.append(float(tokens[3]))
MAGERR_APER.append(float(tokens[4]))
X_IMAGE.append(float(tokens[5]))
Y_IMAGE.append(float(tokens[6]))
if 1159<=float(tokens[5])<=1168:
if 976<=float(tokens[6])<=986:
NUMBER.append(float(tokens[0]))
FLUX_APER.append(float(tokens[1]))
FLUXERR_APER.append(float(tokens[2]))
MAG_APER.append(float(tokens[3]))
MAGERR_APER.append(float(tokens[4]))
X_IMAGE.append(float(tokens[5]))
Y_IMAGE.append(float(tokens[6]))
#Comparison Star 1
if 731<=float(tokens[5])<=740:
if 1044<=float(tokens[6])<=1054:
NUMBER_C1.append(float(tokens[0]))
FLUX_APER_C1.append(float(tokens[1]))
FLUXERR_APER_C1.append(float(tokens[2]))
MAG_APER_C1.append(float(tokens[3]))
MAGERR_APER_C1.append(float(tokens[4]))
X_IMAGE_C1.append(float(tokens[5]))
Y_IMAGE_C1.append(float(tokens[6]))
if 1280<=float(tokens[5])<=1290:
if 967<=float(tokens[6])<=977:
NUMBER_C1.append(float(tokens[0]))
FLUX_APER_C1.append(float(tokens[1]))
FLUXERR_APER_C1.append(float(tokens[2]))
MAG_APER_C1.append(float(tokens[3]))
MAGERR_APER_C1.append(float(tokens[4]))
X_IMAGE_C1.append(float(tokens[5]))
Y_IMAGE_C1.append(float(tokens[6]))
#Comparison Star 2
if 900<=float(tokens[5])<=910:
if 1225<=float(tokens[6])<=1232:
NUMBER_C2.append(float(tokens[0]))
FLUX_APER_C2.append(float(tokens[1]))
FLUXERR_APER_C2.append(float(tokens[2]))
MAG_APER_C2.append(float(tokens[3]))
MAGERR_APER_C2.append(float(tokens[4]))
X_IMAGE_C2.append(float(tokens[5]))
Y_IMAGE_C2.append(float(tokens[6]))
if 1112<=float(tokens[5])<=1125:
if 788<=float(tokens[6])<=798:
NUMBER_C2.append(float(tokens[0]))
FLUX_APER_C2.append(float(tokens[1]))
FLUXERR_APER_C2.append(float(tokens[2]))
MAG_APER_C2.append(float(tokens[3]))
MAGERR_APER_C2.append(float(tokens[4]))
X_IMAGE_C2.append(float(tokens[5]))
Y_IMAGE_C2.append(float(tokens[6]))
#Comparison Star 3
if 825<=float(tokens[5])<=831:
if 926<=float(tokens[6])<=935:
NUMBER_C3.append(float(tokens[0]))
FLUX_APER_C3.append(float(tokens[1]))
FLUXERR_APER_C3.append(float(tokens[2]))
MAG_APER_C3.append(float(tokens[3]))
MAGERR_APER_C3.append(float(tokens[4]))
X_IMAGE_C3.append(float(tokens[5]))
Y_IMAGE_C3.append(float(tokens[6]))
if 1188<=float(tokens[5])<=1198:
if 1084<=float(tokens[6])<=1094:
NUMBER_C3.append(float(tokens[0]))
FLUX_APER_C3.append(float(tokens[1]))
FLUXERR_APER_C3.append(float(tokens[2]))
MAG_APER_C3.append(float(tokens[3]))
MAGERR_APER_C3.append(float(tokens[4]))
X_IMAGE_C3.append(float(tokens[5]))
Y_IMAGE_C3.append(float(tokens[6]))
filein.close()
"""
attempt at adding other stars
#Comparison Star 4
if 547<=float(tokens[5])<=560:
if 1220<=float(tokens[6])<=1234:
NUMBER_C4.append(float(tokens[0]))
FLUX_APER_C4.append(float(tokens[1]))
FLUXERR_APER_C4.append(float(tokens[2]))
MAG_APER_C4.append(float(tokens[3]))
MAGERR_APER_C4.append(float(tokens[4]))
X_IMAGE_C4.append(float(tokens[5]))
Y_IMAGE_C4.append(float(tokens[6]))
if 1455<=float(tokens[5])<=1465:
if 790<=float(tokens[6])<=800:
NUMBER_C4.append(float(tokens[0]))
FLUX_APER_C4.append(float(tokens[1]))
FLUXERR_APER_C4.append(float(tokens[2]))
MAG_APER_C4.append(float(tokens[3]))
MAGERR_APER_C4.append(float(tokens[4]))
X_IMAGE_C4.append(float(tokens[5]))
Y_IMAGE_C4.append(float(tokens[6])) """
#print(FLUX_APER)
#print(FLUXERR_APER)
#print(MAG_APER)
#print(MAGERR_APER)
#print(NUMBER)
#print(X_IMAGE)
#print(Y_IMAGE)
#print(len(X_IMAGE_C1))
#print(len(NUMBER_C1))
#print(len(X_IMAGE_C2))
#print(len(NUMBER_C2))
#print(len(X_IMAGE_C3))
#change lists to arrays
FLUX_APER=np.array(FLUX_APER)
FLUXERR_APER=np.array(FLUXERR_APER)
MAG_APER=np.array(MAG_APER)
MAGERR_APER=np.array(MAGERR_APER)
FLUX_APER_C1=np.array(FLUX_APER_C1)
FLUXERR_APER_C1=np.array(FLUXERR_APER_C1)
MAG_APER_C1=np.array(MAG_APER_C1)
MAGERR_APER_C1=np.array(MAGERR_APER_C1)
FLUX_APER_C2=np.array(FLUX_APER_C2)
FLUXERR_APER_C2=np.array(FLUXERR_APER_C2)
MAG_APER_C2=np.array(MAG_APER_C2)
MAGERR_APER_C2=np.array(MAGERR_APER_C2)
FLUX_APER_C3=np.array(FLUX_APER_C3)
FLUXERR_APER_C3=np.array(FLUXERR_APER_C3)
MAG_APER_C3=np.array(MAG_APER_C3)
MAGERR_APER_C3=np.array(MAGERR_APER_C3)
#read in times
filein = open(tfile, "r")
t = []
for line in filein.readlines(): #iterates through the lines in the file
#tokens = line.split() # breaks line into tokens seperated by ,
#print(tokens)
t.append(float(line))
print('read (past) in files')
t=np.array(t)
dataf=[t,FLUX_APER,FLUXERR_APER,FLUX_APER_C1,FLUXERR_APER_C1,FLUX_APER_C2,FLUXERR_APER_C2,FLUX_APER_C3,FLUXERR_APER_C3]
datam=[t,MAG_APER,MAGERR_APER,MAG_APER_C1,MAGERR_APER_C1,MAG_APER_C2,MAGERR_APER_C2,MAG_APER_C3,MAGERR_APER_C3]
return dataf,datam
def magplot(dataf,datam):
# Plots
t,MAG_APER,MAGERR_APER,MAG_APER_C1,MAGERR_APER_C1,MAG_APER_C2,MAGERR_APER_C2,MAG_APER_C3,MAGERR_APER_C3=datam
t,FLUX_APER,FLUXERR_APER,FLUX_APER_C1,FLUXERR_APER_C1,FLUX_APER_C2,FLUXERR_APER_C2,FLUX_APER_C3,FLUXERR_APER_C3=dataf
# plotting magnitudes and flux of wasp
plt.rcParams["font.family"] = "serif"
plt.minorticks_on()
plt.tick_params(which='major', direction='in', length=6, width=2, colors='black', top=True, right=True)
plt.tick_params(which='minor', length=4, direction='in', top=True, right=True)
plt.scatter(t,MAG_APER)
plt.xlabel("time since transit [days]")
plt.ylabel("Magnitude")
plt.title('WASP Observed Magnitude')
plt.show()
plt.plot(t,FLUX_APER)
plt.xlabel("time since transit [days]")
plt.ylabel("Flux")
plt.title("Wasp Observed Flux")
#plt.axvline(-0.0274,color='r') #telescope flip
#plt.axvline(-0.0297,color='y') #start transit
#plt.axvline(0.0377,color='y')#end transit
#plt.axvline(-0.0297,color='k') #45 sec exposure
#plt.axvline(0.0,color='k') #30 sec exposure
plt.show()
# plotting fluxes and comparison stars of comparison stars next to WASP
plt.plot(t,MAG_APER,label='WASP-2')
plt.plot(t,MAG_APER_C1,label='C1')
plt.plot(t,MAG_APER_C2,label='C2')
plt.plot(t,MAG_APER_C3,label='C3')
#plt.axvline(-0.0274,color='r') #telescope flip
#plt.axvline(-0.0297,color='y') #start transit
#plt.axvline(0.0377,color='y') #end transit
plt.xlabel("time since transit [days]")
plt.ylabel("Magnitude")
plt.legend()
plt.title("Field Star Magnitudes")
plt.show()
def oFluxPlot(data):
# oFluxPlot(data) plots observed flux during observation (counts per second from scaled images)
t,FLUX_APER,FLUXERR_APER,FLUX_APER_C1,FLUXERR_APER_C1,FLUX_APER_C2,FLUXERR_APER_C2,FLUX_APER_C3,FLUXERR_APER_C3=data
plt.errorbar(t,FLUX_APER,yerr=FLUXERR_APER,ecolor='k',label='Wasp2')
plt.errorbar(t,FLUX_APER_C1,yerr=FLUXERR_APER_C1,ecolor='orange', label='$C_1$')
plt.errorbar(t,FLUX_APER_C2,yerr=FLUXERR_APER_C2,ecolor='g', label='$C_2$')
plt.errorbar(t,FLUX_APER_C3,yerr=FLUXERR_APER_C3,ecolor='r', label='$C_3$')
plt.xlabel("time since transit [days]")
plt.ylabel("Flux (counts s$^{-1}$)")
plt.axvline(-0.0377,color='y')
plt.axvline(0.0377,color='y')
plt.title("Observed flux of transit observation")
plt.legend()
plt.show()
def const_flux_plot(dataf,datam):
# const_flux_plot(dataf,datam) see if the comparison stars flux and magnitudes subtracted really give straight lines
t,MAG_APER,MAGERR_APER,MAG_APER_C1,MAGERR_APER_C1,MAG_APER_C2,MAGERR_APER_C2,MAG_APER_C3,MAGERR_APER_C3=datam
t,FLUX_APER,FLUXERR_APER,FLUX_APER_C1,FLUXERR_APER_C1,FLUX_APER_C2,FLUXERR_APER_C2,FLUX_APER_C3,FLUXERR_APER_C3=dataf
MAG_12 = MAG_APER_C1-MAG_APER_C2
plt.plot(t,MAG_12)
MAG_13 = MAG_APER_C1-MAG_APER_C3
plt.plot(t,MAG_13)
MAG_23 = MAG_APER_C2-MAG_APER_C3
plt.plot(t,MAG_23)
MAG_Extinc = MAG_APER-MAG_APER_C1
plt.plot(t, MAG_Extinc)
plt.title("Mag subtract")
plt.show()
FLUX_12 = FLUX_APER_C1/FLUX_APER_C2
err_12 = div_err(FLUX_APER_C1,FLUX_APER_C2,FLUXERR_APER_C1,FLUXERR_APER_C2)
FLUX_13 = FLUX_APER_C1/FLUX_APER_C3
FLUX_23 = FLUX_APER_C2/FLUX_APER_C3
FLUX_21 = FLUX_APER_C2/FLUX_APER_C1
FLUX_31 = FLUX_APER_C3/FLUX_APER_C1
FLUX_32 = FLUX_APER_C3/FLUX_APER_C2
plt.errorbar(t,FLUX_12, yerr=err_12, ecolor='k', label='$C_1/C_2 w err$')
plt.plot(t,FLUX_13, label='$C_1/C_3$')
plt.plot(t,FLUX_23, label='$C_2/C_3$')
plt.plot(t,FLUX_23, label='$C_2/C_1$')
plt.plot(t,FLUX_31, label='$C_3/C_1$')
plt.plot(t,FLUX_32, label='$C_3/C_2$')
plt.xlabel("time since transit [days]")
plt.ylabel("Flux ratio")
plt.title("Flux ratios of comparison stars")
plt.legend()
plt.show()
def extinction_test(data):
# extinction_test(data) TEST to see how wasp flux reacts to division by comp stars
t,FLUX_APER,FLUXERR_APER,FLUX_APER_C1,FLUXERR_APER_C1,FLUX_APER_C2,FLUXERR_APER_C2,FLUX_APER_C3,FLUXERR_APER_C3=data
FLUX_Extinc = FLUX_APER/FLUX_APER_C1
FLUX_Extinc2 = FLUX_APER/FLUX_APER_C2
FLUX_Extinc3 = FLUX_APER/FLUX_APER_C3
plt.plot(t, FLUX_Extinc, label='$W/C_1$')
plt.plot(t, FLUX_Extinc2, label='$W/C_2$')
plt.plot(t, FLUX_Extinc3, label='$W/C_3$')
plt.title("Flux ratio of WASP/Comparison Stars")
plt.xlabel("time since transit [days]")
plt.ylabel("Flux ratio")
plt.legend()
plt.show()
def AtEx(data):
# determine the mean of comparison star fluxes and divide the flux by mean to get the atmospheric fluctuations from the mean
# find the weighted average flux fluctuation from all comparison stars
# WASP flux adjusted for extinction
# Determine error on WASP as combo of observed wasp errors and reduced flux fluct errors
# find average flux of WASP2 not during transit to use for normalisation
# normalise WASP flux and compute errors
t,FLUX_APER,FLUXERR_APER,FLUX_APER_C1,FLUXERR_APER_C1,FLUX_APER_C2,FLUXERR_APER_C2,FLUX_APER_C3,FLUXERR_APER_C3=data
C1_mean_FLUX = np.mean(FLUX_APER_C1)
#print(np.std(FLUX_APER_C1)/np.sqrt(len(FLUX_APER_C1))) # error on the mean is 1.6 << FLUXERR so ignored
C1_Fluct_FLUX = FLUX_APER_C1 / C1_mean_FLUX # to do: calc error on the mean, standard deviation
c1err= div_err(FLUX_APER_C1,C1_mean_FLUX,FLUXERR_APER_C1,0)
C2_mean_FLUX = np.mean(FLUX_APER_C2)
C2_Fluct_FLUX = FLUX_APER_C2 / C2_mean_FLUX
c2err= div_err(FLUX_APER_C2,C2_mean_FLUX,FLUXERR_APER_C2,0)
C3_mean_FLUX = np.mean(FLUX_APER_C3)
C3_Fluct_FLUX = FLUX_APER_C3 / C3_mean_FLUX
c3err= div_err(FLUX_APER_C3,C3_mean_FLUX,FLUXERR_APER_C3,0)
# find the weighted mean flux fluctuation (and error) from all comparison stars
AVG_FLUX_FLUCT,avgerr = w_mean(C1_Fluct_FLUX,C2_Fluct_FLUX,C3_Fluct_FLUX,c1err,c2err,c3err)
# WASP flux adjusted for extinction
Flux_WASP=FLUX_APER/AVG_FLUX_FLUCT
# Determine error on WASP as combo of observed wasp errors and reduced flux fluct errors
fwerr=div_err(FLUX_APER,AVG_FLUX_FLUCT,FLUXERR_APER,avgerr)
# find average flux of WASP2 not during transit to use for normalisation
# before transit values 0:9, 140:178
index = np.arange(10,139,step=1) #transit images 10-139 for maybe data, 6-129 for sure data
WASP_outsidetransit = np.mean(np.delete(Flux_WASP,index)) # calculate std for mean error
#print(np.std(np.delete(Flux_WASP,index))/np.sqrt(len(np.delete(Flux_WASP,index)))) # error on the mean is 1.6 << fwerr so ignored
# normalise WASP flux and compute errors
Flux_WASP_normal = Flux_WASP/WASP_outsidetransit
fwnerr = (fwerr/Flux_WASP)*Flux_WASP_normal
'''
plt.rcParams["font.family"] = "serif"
plt.minorticks_on()
plt.tick_params(which='major', direction='in', length=6, width=2, colors='black', top=True, right=True)
plt.tick_params(which='minor', length=4, direction='in', top=True, right=True)
plt.plot(t,FLUX_APER_C1,label='$C_1$',color='red')
plt.plot(t,FLUX_APER_C2, label='$C_2$',color='blue')
plt.plot(t,FLUX_APER_C3, label='$C_3$',color='darkgrey')
plt.hlines(C1_mean_FLUX,min(t),max(t),color='darkred')
plt.hlines(C2_mean_FLUX,min(t),max(t), color='darkblue')
plt.hlines(C3_mean_FLUX,min(t),max(t),color='k')
#plt.plot(t, AVG_FLUX_FLUCT)
plt.title("Observed and Mean Flux of Comparison Field Stars")
plt.xlabel("Time since mid-transit [days]")
plt.ylabel("Flux (counts s$^{-1}$)")
plt.legend()
plt.show()
plt.plot(t,C1_Fluct_FLUX, label='$C_1$')
plt.plot(t,C2_Fluct_FLUX, label='$C_2$')
plt.plot(t,C3_Fluct_FLUX, label='$C_3$')
plt.plot(t, AVG_FLUX_FLUCT,color='k',label='Mean')
plt.title("Ratio of flux extinction from comparison field stars")
plt.xlabel("time since mid-transit [days]")
plt.ylabel("flux ratio: f$_{obs}/f_{mean}$")
plt.legend()
plt.show()
'''
#Comparison Stars corrected for extinction, should give straight lines
Flux_C1=FLUX_APER_C1/AVG_FLUX_FLUCT
Flux_C2=FLUX_APER_C2/AVG_FLUX_FLUCT
Flux_C3=FLUX_APER_C3/AVG_FLUX_FLUCT
plt.rcParams["font.family"] = "serif"
plt.minorticks_on()
plt.tick_params(which='major', direction='in', length=6, width=2, colors='black', top=True, right=True)
plt.tick_params(which='minor', length=4, direction='in', top=True, right=True)
plt.plot(t,Flux_C1,label='$C_1$ corr',lw=1)
plt.plot(t,Flux_C2,label='$C_2$ corr',lw=1)
plt.plot(t,Flux_C3,label='$C_3$ corr',lw=1)
#plt.plot(t,FLUX_APER_C1, label='$C_1$ obs',color='red')
#plt.plot(t,FLUX_APER_C2, label='$C_2$ obs',color='blue')
#plt.plot(t,FLUX_APER_C3, label='$C_3$ obs',color='k')
#plt.axvline(-0.0377,color='y') #start transit
#plt.axvline(0.0377,color='y')#end transit
plt.title("Comparison Star Atmos.Corrected Fluxes")
plt.xlabel("Time since mid-transit [days]")
plt.ylabel("Flux (counts s$^{-1}$)")
plt.legend()
plt.show()
plt.rcParams["font.family"] = "serif"
plt.minorticks_on()
plt.tick_params(which='major', direction='in', length=6, width=2, colors='black', top=True, right=True)
plt.tick_params(which='minor', length=4, direction='in', top=True, right=True)
#plt.axvline(-0.0274,color='r') #telescope flip
#plt.axvline(-0.0377,color='y') #start transit
#plt.axvline(0.0377,color='y')#end transit
#plt.axvline(-0.0297,color='k') #45 sec exposure
#plt.axvline(0.0,color='k') #30 sec exposure
plt.plot(t,FLUX_APER,label='observed',color='k',lw=1)
plt.plot(t,Flux_WASP,label='corrected',color='red',lw=1)
plt.title("Wasp Observed Flux vs Wasp Corrected Flux")
plt.xlabel("time since transit [days]")
plt.ylabel("Flux (counts s$^{-1}$)")
plt.ylim(ymin=2950,ymax=3100)
plt.legend()
plt.show()
return Flux_WASP_normal,fwnerr
### Plotting the Model ###
# different models for different fixed parameters
def batmanCurveFit0(xdata,rp0,inc0,e0,w0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = e0 #eccentricity
params.w = w0 #longitude of periastron (in degrees)
params.limb_dark = "uniform" #limb darkening model
params.u = [] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFitee0(xdata,rp0,inc0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "uniform" #limb darkening model
params.u = [] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFit1(xdata,rp0,inc0,e0,w0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = e0 #eccentricity
params.w = w0 #longitude of periastron (in degrees)
params.limb_dark = "linear" #limb darkening model
params.u = [0.525] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFite1(xdata,rp0,inc0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "linear" #limb darkening model
params.u = [0.525] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFit2(xdata,rp0,inc0,e0,w0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = e0 #eccentricity
params.w = w0 #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFite2(xdata,rp0,inc0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFit3(xdata,rp0,inc0,e0,w0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = e0 #eccentricity
params.w = w0 #longitude of periastron (in degrees)
params.limb_dark = "nonlinear" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFite3(xdata,rp0,inc0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "nonlinear" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFitAllFree(xdata,rp0,inc0,e0,w0,T0,a0):
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = T0 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = a0 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = e0 #eccentricity
params.w = w0 #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFitTmax(xdata,rp0,inc0): # Tmax , a_mean
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFitTmin(xdata,rp0,inc0,e0,w0): # Tmin , a_mean
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFitAmax(xdata,rp0,inc0,e0,w0): # Tmean , a_max
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFitAmin(xdata,rp0,inc0,e0,w0): # Tmean , a_min
params = batman.TransitParams()
#rp0,inc0,e0,w0=ig
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def batmanCurveFite0(xdata,rp0,inc0):
params = batman.TransitParams()
params.t0 = 0. #time of inferior conjunction
params.per = 2.148 #orbital period days
params.rp = rp0 #planet radius (in units of stellar radii)
params.a = 8.296 #semi-major axis (in units of stellar radii)
params.inc = inc0 #orbital inclination (in degrees)
params.ecc = 0.069 #eccentricity
params.w = 90. #longitude of periastron (in degrees)
params.limb_dark = "quadratic" #limb darkening model
params.u = [0.525, 0.188] #limb darkening coefficients [u1, u2]
m = batman.TransitModel(params, xdata)
flux = m.light_curve(params)
return flux
def AllVarParams(t,Wflux,nWerr):
# a function to plot the best fit curve allowing all parameters to be free with strict boundary conditions
ig=[0.135,84.7,0.,0.,2.152060692723822,8.308334998763279] # final 2, period and semi-major axis, calculated from RV data
s_err=scaleError(nWerr,4.5) # scale errors
lbound=[0.,0.,0.,0.,2.151805365,8.291457176] # lower error from RV data
ubound=[1.,90.,1.,180.,2.152316018,8.37161626187] # upper error from RV data
fitThis = spicy.curve_fit(f = batmanCurveFitAllFree, xdata = t, ydata = Wflux, sigma=s_err, p0=ig, bounds=(lbound,ubound))
abest,bbest,cbest,dbest,ebest,fbest = fitThis[0]
aerr = np.sqrt(fitThis[1][0][0])
berr = np.sqrt(fitThis[1][1][1])
cerr = np.sqrt(fitThis[1][2][2])
derr = np.sqrt(fitThis[1][3][3])
eerr = np.sqrt(fitThis[1][4][4])
ferr = np.sqrt(fitThis[1][5][5])
#flux=batmanCurveFit3(t,abest,bbest,cbest,dbest)
#plt.plot(t, flux, label = ld[3]) # model
print('\033[1m')#+'Limb Darkening model: \'%s\''%ld[3]+'\033[0m')
print('Planet Radius (stellar radius): %s +/- %s'%(abest,aerr))
print('Oribital Inclination (degrees): %s +/- %s'%(bbest,berr))
print('Eccentrcity: %s +/- %s'%(cbest,cerr))
print('Longitude of periapsis (degrees): %s +/- %s'%(dbest,derr))
print('Orbital Period (days): %s +/- %s'%(ebest,eerr))
print('Semi-major axis (a) [R_wasp]: %s +/- %s'%(fbest,ferr))
print('\033[0m')
params=fitThis[0]
variance=[aerr,berr,cerr,derr,eerr,ferr]
return params,variance
def LDModels(t,data,err,ig):
# plot figure comparing limb darkening models
#ig=np.array([0.13,0,0.8,0]) # Rp (R_wasp), orbital inclination, eccentricity, longitude of periapsis
s_err=scaleError(err,4.5)
ld = ["uniform", "linear", "quadratic"]#, "nonlinear"]
funcs=[batmanCurveFit0,batmanCurveFit1,batmanCurveFit2] #,batmanCurveFit3]
plt.figure()
plt.errorbar(t, data ,yerr=s_err,color='blue',ecolor='k',zorder=1,fmt='.',ms=1.5,elinewidth=0.15)
##### uniform fit #####
for i in range(len(funcs)):
fitThis=spicy.curve_fit(f = funcs[i], xdata = t, ydata = data, sigma=s_err, p0=ig, bounds=(0,[1.,90.,1.,360.]))
abest, bbest,cbest,dbest = fitThis[0]
aerr = np.sqrt(fitThis[1][0][0])
berr = np.sqrt(fitThis[1][1][1])
cerr = np.sqrt(fitThis[1][2][2])
derr = np.sqrt(fitThis[1][3][3])
flux=funcs[i](t,abest,bbest,cbest,dbest)
plt.plot(t, flux, label = ld[i]) # model
print('\033[1m'+'Limb Darkening model: \'%s\''%ld[i]+'\033[0m')
print('Planet Radius (stellar radius): %s +/- %s'%(abest,aerr))
print('Oribital Inclination (degrees): %s +/- %s'%(bbest,berr))
print('Ellipticity: %s +/- %s'%(cbest,cerr))
print('Longitude of periapsis (degrees): %s %s'%(dbest,derr))
#plt.ylim(0.98, 1.01)
plt.xlabel("time since transit [days]")
plt.ylabel("relative flux")
plt.legend()
plt.show()
def LDeModels(t,data,err,ig):
# plot figure comparing limb darkening models
#ig=np.array([0.13,0,0.8,0]) # Rp (R_wasp), orbital inclination, eccentricity, longitude of periapsis
s_err=scaleError(err,4.5)
ld = ["uniform", "linear", "quadratic"] #, "nonlinear"]
ld_coefficients = [[], [0.525], [0.525, 0.188]]
funcs=[batmanCurveFitee0,batmanCurveFite1,batmanCurveFite2]#,batmanCurveFite3]
cs=["red","lawngreen","k"]
plt.rcParams["font.family"] = "serif"
plt.figure()
plt.errorbar(t, data ,yerr=s_err,color='blue',ecolor='k',zorder=1,fmt='.',ms=1.5,elinewidth=0.15)
for i in range(len(funcs)):
##### uniform fit, linear fit, quadratic fit, nonlinear fit #####
fitThis=spicy.curve_fit(f = funcs[i], xdata = t, ydata = data, sigma=s_err, p0=ig, bounds=(0,[1.,90.]))
abest, bbest = fitThis[0]
aerr = np.sqrt(fitThis[1][0][0])
berr = np.sqrt(fitThis[1][1][1])
#cerr = np.sqrt(fitThis[1][2][2])
flux=funcs[i](t,abest,bbest)
print('\033[1m'+'Limb Darkening model: \'%s\''%ld[i]+'\033[0m')
print('Planet Radius (stellar radius): %s +/- %s'%(abest,aerr))
print('Oribital Inclination (degrees): %s +/- %s'%(bbest,berr))
#print('Longitude of periapsis (degrees): %s %s'%(cbest,cerr))
rcs=chsq(data,flux,s_err,[abest,bbest])
plt.plot(t, flux, color=cs[i], label = ld[i]+', $\chi_\\nu^2$=%.3f'%rcs,lw=1)
plt.minorticks_on()