In [1]:

    

from scipy.optimize import curve_fit
import astropy.io.ascii as ascii
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np


    

In [2]:

    

tab1=ascii.read("Table1.csv")
tab2=ascii.read("Table2.csv")
tab3=ascii.read("Table3.csv")


    

In [3]:

    

tab1


    

    
Out[3]:




<Table length=21>

radius
rvel
Theoryval
Ydiffval
rvelerr
float64
float64
float64
float64
float64
0.215827338129
12.9
9.0
3.9
1.8
0.44964028777
17.1
10.8
6.3
1.8
0.647482014388
23.7
11.85
11.85
1.8
0.89928057554
26.4
12.0
14.4
1.8
1.18705035971
27.6
12.0
15.6
1.8
1.36690647482
27.0
11.55
15.45
1.8
1.61870503597
27.6
11.55
16.05
1.8
1.8345323741
31.2
11.55
19.65
1.8
2.05035971223
32.7
11.4
21.3
1.8
2.26618705036
33.3
11.55
21.75
1.8
2.55395683453
37.2
12.15
25.05
1.8
2.76978417266
39.0
12.6
26.4
1.8
3.23741007194
41.7
13.2
28.5
1.8
3.72302158273
43.2
13.5
29.7
1.8
4.20863309353
45.3
14.1
31.2
1.8
4.64028776978
47.1
14.4
32.7
1.8
5.10791366906
49.2
14.7
34.5
1.8
5.59352517986
50.4
14.7
35.7
1.8
6.04316546763
50.7
14.7
36.0
1.8
6.52877697842
51.0
14.4
36.6
1.95
7.01438848921
52.35
14.1
38.25
2.7

In [4]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['rvel'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
plt.plot(tab1['radius'],tab1['Theoryval'],'-')
plt.plot(tab1['radius'],tab1['Ydiffval'],'--')
plt.title('Gas Dominated Dwarf (NGC 3741)')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('gasdwarf.pdf')
plt.savefig('gasdwarf.jpeg')


    

In [5]:

    

def line(x, a):
    return a * x


    

In [6]:

    

popt, pcov = curve_fit(line, tab1['radius'], tab1['Ydiffval'])


    

In [7]:

    

popt


    

    
Out[7]:





array([ 6.85024949])

In [8]:

    

pcov


    

    
Out[8]:





array([[ 0.13622374]])

In [10]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['Ydiffval'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 7.5, 100)  # define values to plot the function for
plt.plot(xfine, line(xfine, popt), 'r-')
plt.title('Gas Dominated Dwarf best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('gasdwarf_fit_omega.pdf')
plt.savefig('gasdwarf_fit_omega.jpeg')


    

In [11]:

    

tab2


    

    
Out[11]:




<Table length=31>

Radius
Rvelocity
Theory
Veldiff
Velerr
float64
float64
float64
float64
float64
0.616438356164
77.4725274725
51.6483516484
25.8241758242
10.4395604396
1.43835616438
100.0
89.010989011
10.989010989
3.2967032967
2.19178082192
109.89010989
100.549450549
9.34065934066
3.2967032967
2.87671232877
118.131868132
96.1538461538
21.978021978
3.2967032967
3.69863013699
121.428571429
86.8131868132
34.6153846154
3.2967032967
4.45205479452
121.428571429
81.3186813187
40.1098901099
3.2967032967
5.20547945205
117.582417582
74.1758241758
43.4065934066
3.2967032967
5.61643835616
116.483516484
72.5274725275
43.956043956
3.2967032967
6.09589041096
115.934065934
70.3296703297
45.6043956044
3.2967032967
6.84931506849
115.934065934
66.4835164835
49.4505494505
3.2967032967
...
...
...
...
...
15.0684931507
117.582417582
51.6483516484
65.9340659341
3.2967032967
15.8904109589
115.934065934
50.5494505495
65.3846153846
3.2967032967
16.5753424658
114.835164835
50.0
64.8351648352
3.2967032967
17.397260274
114.835164835
48.9010989011
65.9340659341
3.2967032967
18.1506849315
114.835164835
47.8021978022
67.032967033
3.2967032967
19.5205479452
114.835164835
46.1538461538
68.6813186813
3.2967032967
20.9589041096
115.934065934
45.0549450549
70.8791208791
3.2967032967
21.8493150685
114.835164835
43.956043956
70.8791208791
4.3956043956
22.6712328767
118.131868132
43.4065934066
74.7252747253
4.3956043956
23.4246575342
116.483516484
42.3076923077
74.1758241758
10.4395604396

In [12]:

    

plt.figure()
plt.errorbar(tab2['Radius'],tab2['Rvelocity'],yerr=tab2['Velerr'],fmt='o',capsize=3)
plt.plot(tab2['Radius'],tab2['Theory'],'-')
plt.plot(tab2['Radius'],tab2['Veldiff'],'--')
plt.title('Disk-Dominated Spiral (NGC6503)')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('diskspiral.pdf')
plt.savefig('diskspiral.jpeg')


    

In [13]:

    

popt2, pcov2 = curve_fit(line, tab2['Radius'], tab2['Veldiff'])


    

In [15]:

    

plt.figure()
plt.errorbar(tab2['Radius'],tab2['Veldiff'],yerr=tab2['Velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 25, 100)  # define values to plot the function for
plt.plot(xfine, line(xfine, popt2), 'r-')
plt.title('Disk-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('diskspiral_fit_omega.pdf')
plt.savefig('diskspiral_fit_omega.jpeg')


    

In [16]:

    

print popt2
print pcov2


    

    




[ 4.1327069]
[[ 0.04702947]]

In [17]:

    

tab3


    

    
Out[17]:




<Table length=18>

radius
rvel
Rtheory
veldiff
velerr
float64
float64
float64
float64
float64
1.59482758621
255.833333333
276.666666667
-20.8333333333
14.1666666667
1.76724137931
241.666666667
246.666666667
-5.0
14.1666666667
2.80172413793
224.166666667
220.0
4.16666666667
6.66666666667
3.87931034483
220.833333333
199.166666667
21.6666666667
6.66666666667
5.04310344828
219.166666667
184.166666667
35.0
6.66666666667
6.12068965517
219.166666667
170.0
49.1666666667
6.66666666667
7.19827586207
218.333333333
158.333333333
60.0
6.66666666667
8.23275862069
216.666666667
150.0
66.6666666667
5.0
9.35344827586
213.333333333
142.5
70.8333333333
5.0
10.474137931
211.666666667
135.833333333
75.8333333333
5.0
11.5086206897
207.5
130.0
77.5
5.0
12.4568965517
205.833333333
125.0
80.8333333333
5.0
13.7068965517
206.666666667
119.166666667
87.5
5.0
14.7413793103
205.833333333
115.0
90.8333333333
5.0
15.775862069
205.0
111.666666667
93.3333333333
5.0
16.9396551724
205.0
108.333333333
96.6666666667
5.0
17.974137931
204.166666667
104.166666667
100.0
5.0
19.0517241379
205.0
100.833333333
104.166666667
5.0

In [18]:

    

plt.figure()
plt.errorbar(tab3['radius'],tab3['rvel'],yerr=tab3['velerr'],fmt='o',capsize=3)
plt.plot(tab3['radius'],tab3['Rtheory'],'-')
plt.plot(tab3['radius'],tab3['veldiff'],'--')
plt.title('Bulge-Dominated Spiral (NGC7814)')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('bulgespiral.pdf')
plt.savefig('bulgespiral.jpeg')


    

In [19]:

    

popt3, pcov3 = curve_fit(line, tab3['radius'], tab3['veldiff'])


    

In [20]:

    

plt.figure()
plt.errorbar(tab3['radius'],tab3['veldiff'],yerr=tab3['velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 20, 100)  # define values to plot the function for
plt.plot(xfine, line(xfine, popt3), 'r-')
plt.title('Bulge-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('bulgespiral_fit_omega.pdf')
plt.savefig('bulgespiral_fit_omega.jpeg')


    

In [21]:

    

print popt3
print pcov3


    

    




[ 6.15506884]
[[ 0.06964819]]

In [91]:

    

popt, pcov = curve_fit(line, tab1['radius'][2:], tab1['Ydiffval'][2:])


    

In [90]:

    

tab1['radius'][2:]


    

    
Out[90]:




<Column name='radius' dtype='float64' length=19>

0.647482014388
0.89928057554
1.18705035971
1.36690647482
1.61870503597
1.8345323741
2.05035971223
2.26618705036
2.55395683453
2.76978417266
3.23741007194
3.72302158273
4.20863309353
4.64028776978
5.10791366906
5.59352517986
6.04316546763
6.52877697842
7.01438848921

In [93]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['Ydiffval'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 7.5, 100)  # define values to plot the function for
plt.plot(xfine, line(xfine, popt[0], popt[1]), 'r-')
plt.title('Gas Dominated Dwarf best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Diff between theory & observed (in km/s/Mpc)')
plt.savefig('gasdwarf_diff_fit.pdf')
plt.savefig('gasdwarf_diff_fit.jpeg')


    

In [95]:

    

popt2, pcov2 = curve_fit(line, tab2['Radius'][4:], tab2['Veldiff'][4:])
plt.figure()
plt.errorbar(tab2['Radius'],tab2['Veldiff'],yerr=tab2['Velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 25, 100)  # define values to plot the function for
plt.plot(xfine, line(xfine, popt2[0], popt2[1]), 'r-')
plt.title('Disk-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Diff between theory & observed (in km/s/Mpc)')
plt.savefig('diskspiral_diff_fit.pdf')
plt.savefig('diskspiral_diff_fit.jpeg')


    

In [96]:

    

popt3, pcov3 = curve_fit(line, tab3['radius'][2:], tab3['veldiff'][2:])
plt.figure()
plt.errorbar(tab3['radius'],tab3['veldiff'],yerr=tab3['velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 20, 100)  # define values to plot the function for
plt.plot(xfine, line(xfine, popt3[0], popt3[1]), 'r-')
plt.title('Bulge-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Diff between theory & observed (in km/s/Mpc)')
plt.savefig('bulgespiral_diff_fit.pdf')
plt.savefig('bulgespiral_diff_fit.jpeg')


    

In [22]:

    

def linexp(x, a, b):
    return a * x * np.exp(b*x)


    

In [23]:

    

popt, pcov = curve_fit(linexp, tab1['radius'], tab1['Ydiffval'])


    

In [24]:

    

print popt


    

    




[ 13.87255675  -0.13957306]

In [26]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['Ydiffval'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 7.5, 100)  # define values to plot the function for
plt.plot(xfine, linexp(xfine, popt[0], popt[1]), 'r-')
plt.title('Gas Dominated Dwarf best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('gasdwarf_fit_omega_exp.pdf')
plt.savefig('gasdwarf_fit_omega_exp.jpeg')


    

In [29]:

    

popt2, pcov2 = curve_fit(linexp, tab2['Radius'], tab2['Veldiff'])


    

In [30]:

    

print popt2
print pcov2


    

    




[ 9.69318051 -0.05125356]
[[  2.03556902e-01  -1.26896768e-03]
 [ -1.26896768e-03   9.06721199e-06]]

In [32]:

    

plt.figure()
plt.errorbar(tab2['Radius'],tab2['Veldiff'],yerr=tab2['Velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 25, 100)  # define values to plot the function for
plt.plot(xfine, linexp(xfine, popt2[0], popt2[1]), 'r-')
plt.title('Disk-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('diskspiral_fit_omega_exp.pdf')
plt.savefig('diskspiral_fit_omega_exp.jpeg')


    

In [33]:

    

popt3, pcov3 = curve_fit(linexp, tab3['radius'], tab3['veldiff'])


    

In [34]:

    

plt.figure()
plt.errorbar(tab3['radius'],tab3['veldiff'],yerr=tab3['velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 20, 100)  # define values to plot the function for
plt.plot(xfine, linexp(xfine, popt3[0], popt3[1]), 'r-')
plt.title('Bulge-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('bulgespiral_fit_omega_exp.pdf')
plt.savefig('bulgespiral_fit_omega_exp.jpeg')


    

In [36]:

    

print popt3
print pcov3


    

    




[ 8.20725534 -0.01978487]
[[  1.35084716e+00  -1.08074934e-02]
 [ -1.08074934e-02   9.36132066e-05]]

In [45]:

    

def linexp1(x, a, b):
    return a * np.exp(b*x)


    

In [46]:

    

popt, pcov = curve_fit(linexp1, tab1['radius'], tab1['Ydiffval'])


    

In [47]:

    

print popt
print pcov


    

    




[ 13.71815518   0.16465184]
[[  1.56248410e+00  -2.09533954e-02]
 [ -2.09533954e-02   3.38885992e-04]]

In [48]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['Ydiffval'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 7.5, 100)  # define values to plot the function for
plt.plot(xfine, linexp1(xfine, popt[0], popt[1]), 'r-')
plt.title('Gas Dominated Dwarf best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('gasdwarf_fit_omega_exp1.pdf')
plt.savefig('gasdwarf_fit_omega_exp1.jpeg')


    

In [49]:

    

popt2, pcov2 = curve_fit(linexp1, tab2['Radius'], tab2['Veldiff'])


    

In [50]:

    

print popt2
print pcov2


    

    




[ 33.57395059   0.03853322]
[[  6.32882197e+00  -1.07957812e-02]
 [ -1.07957812e-02   2.20317898e-05]]

In [51]:

    

plt.figure()
plt.errorbar(tab2['Radius'],tab2['Veldiff'],yerr=tab2['Velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 25, 100)  # define values to plot the function for
plt.plot(xfine, linexp1(xfine, popt2[0], popt2[1]), 'r-')
plt.title('Disk-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('diskspiral_fit_omega_exp1.pdf')
plt.savefig('diskspiral_fit_omega_exp1.jpeg')


    

In [52]:

    

popt3, pcov3 = curve_fit(linexp1, tab3['radius'], tab3['veldiff'])


    

In [53]:

    

plt.figure()
plt.errorbar(tab3['radius'],tab3['veldiff'],yerr=tab3['velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 20, 100)  # define values to plot the function for
plt.plot(xfine, linexp1(xfine, popt3[0], popt3[1]), 'r-')
plt.title('Bulge-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('bulgespiral_fit_omega_exp1.pdf')
plt.savefig('bulgespiral_fit_omega_exp1.jpeg')


    

In [ ]:

    




    

In [54]:

    

def linexp2(x, a, b):
    return a * np.exp(b/x)


    

In [55]:

    

popt, pcov = curve_fit(linexp2, tab1['radius'], tab1['Ydiffval'])


    

In [56]:

    

print popt
print pcov


    

    




[ 42.74594111  -1.25279963]
[[ 2.8838049  -0.16093615]
 [-0.16093615  0.0126969 ]]

In [57]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['Ydiffval'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 7.5, 100)  # define values to plot the function for
plt.plot(xfine, linexp2(xfine, popt[0], popt[1]), 'r-')
plt.title('Gas Dominated Dwarf best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('gasdwarf_fit_omega_exp2.pdf')
plt.savefig('gasdwarf_fit_omega_exp2.jpeg')


    

    




/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in divide
  from ipykernel import kernelapp as app






    

In [58]:

    

popt2, pcov2 = curve_fit(linexp2, tab2['Radius'], tab2['Veldiff'])


    

In [59]:

    

print popt2
print pcov2


    

    




[ 82.94523877  -3.59263564]
[[ 7.08181719 -0.70943047]
 [-0.70943047  0.09845183]]

In [60]:

    

plt.figure()
plt.errorbar(tab2['Radius'],tab2['Veldiff'],yerr=tab2['Velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 25, 100)  # define values to plot the function for
plt.plot(xfine, linexp2(xfine, popt2[0], popt2[1]), 'r-')
plt.title('Disk-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('diskspiral_fit_omega_exp2.pdf')
plt.savefig('diskspiral_fit_omega_exp2.jpeg')


    

    




/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in divide
  from ipykernel import kernelapp as app






    

In [61]:

    

popt3, pcov3 = curve_fit(linexp2, tab3['radius'], tab3['veldiff'])


    

In [62]:

    

plt.figure()
plt.errorbar(tab3['radius'],tab3['veldiff'],yerr=tab3['velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 20, 100)  # define values to plot the function for
plt.plot(xfine, linexp2(xfine, popt3[0], popt3[1]), 'r-')
plt.title('Bulge-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('bulgespiral_fit_omega_exp2.pdf')
plt.savefig('bulgespiral_fit_omega_exp2.jpeg')


    

    




/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in divide
  from ipykernel import kernelapp as app






    

In [ ]:

    




    

In [63]:

    

def linexp3(x, a, b):
    return a *x* np.exp(b/x)


    

In [64]:

    

popt, pcov = curve_fit(linexp3, tab1['radius'], tab1['Ydiffval'])


    

In [65]:

    

print popt
print pcov


    

    




[ 6.2073411   0.44688667]
[[ 0.09905815 -0.0160852 ]
 [-0.0160852   0.00899746]]

In [66]:

    

plt.figure()
plt.errorbar(tab1['radius'],tab1['Ydiffval'],yerr=tab1['rvelerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 7.5, 100)  # define values to plot the function for
plt.plot(xfine, linexp3(xfine, popt[0], popt[1]), 'r-')
plt.title('Gas Dominated Dwarf best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('gasdwarf_fit_omega_exp3.pdf')
plt.savefig('gasdwarf_fit_omega_exp3.jpeg')


    

    




/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in divide
  from ipykernel import kernelapp as app
/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: invalid value encountered in multiply
  from ipykernel import kernelapp as app






    

In [69]:

    

popt2, pcov2 = curve_fit(linexp3, tab2['Radius'], tab2['Veldiff'])


    

In [70]:

    

print popt2
print pcov2


    

    




[ 3.70761512  1.69268452]
[[ 0.02947047 -0.01683011]
 [-0.01683011  0.04805995]]

In [71]:

    

plt.figure()
plt.errorbar(tab2['Radius'],tab2['Veldiff'],yerr=tab2['Velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 25, 100)  # define values to plot the function for
plt.plot(xfine, linexp3(xfine, popt2[0], popt2[1]), 'r-')
plt.title('Disk-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('diskspiral_fit_omega_exp3.pdf')
plt.savefig('diskspiral_fit_omega_exp3.jpeg')


    

    




/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in divide
  from ipykernel import kernelapp as app
/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: invalid value encountered in multiply
  from ipykernel import kernelapp as app






    

In [73]:

    

popt3, pcov3 = curve_fit(linexp3, tab3['radius'], tab3['veldiff'])


    

In [74]:

    

plt.figure()
plt.errorbar(tab3['radius'],tab3['veldiff'],yerr=tab3['velerr'],fmt='o',capsize=3)
xfine = np.linspace(0., 20, 100)  # define values to plot the function for
plt.plot(xfine, linexp3(xfine, popt3[0], popt3[1]), 'r-')
plt.title('Bulge-dominated Spiral best fit')
plt.xlabel('Radius(in kpc)')
plt.ylabel('Rotational velocity (in km/s/Mpc)')
plt.savefig('bulgespiral_fit_omega_exp3.pdf')
plt.savefig('bulgespiral_fit_omega_exp3.jpeg')


    

    




/Users/rohin/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in divide
  from ipykernel import kernelapp as app






    

In [ ]: